allied mat120 full course [ all discussions all homework and all check understanding ]

| August 30, 2017

Question
mod 2

.allied.edu/Images/1×1.gif”> Posted by Christina Holdiness at 05/29/13 12:12 PM
1. Kahn Academy is a website that provides free videos, instruction, and practice for a variety of topics, including math. I want you to read a little more about this website, then use it to find a video or practice exercises that would help you with this week’s concepts.

.khanacademy.org/about”>http://www.khanacade

module 3

Find examples of where Quadratic Equations are used in everyday life and applications. If you find an example in the book, tell us the page. If you find an example online, please provide the link.
mod 4
Identify and discuss a real world application of graphing and the rectangular coordinate system. You may need to search the web for references. Cite any website that you use.

mod 5
Give an example of a relation that you see in your everyday life. Is this relation a function?

mod 6

The Proctor Form for the Final Exam is due this week. Please post below confirming that you are completing and submitting this form by the end of the week.

mod 7

Exponential and logarithmic functions are used in a variety of applications. Why do you believe that it important to study and understand a wide variety of functions and their graphs? Why do we classify functions and give them different names?

mod 8

Which method of solving a System of Linear Equations do you prefer and why? You may prefer a different method depending on the system.

check understanding

week 1

Q

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9.

Factor out, relative to the integers, all factors common to all terms.

18×4 + 21×3 + 21×2

a.3×2(6×2 + 21x + 21)

b.3×2(6×2 + 7x + 7)

c.18×2(x2 + 7x + 7)

d.18x(x3 + 21×2 + 21x)

10.

Simplify. (2a–7b2)–5

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11.

Perform the indicated operations and reduce to lowest terms.

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12.

Perform the indicated operations and simplify. (3x – 1)(2x + 5)

a.6×2 – 13x – 5

b.6×2 – 17x – 5

c.6×2 + 13x – 5

d.6×2 + 17x – 5

13.

Evaluate the expression if it is a real number. .0/msohtmlclip1/01/clip_image025.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/6087e584-dd1a-4186-94cf-661d18ede1f1.gif”>

a. 45

b. 9

c. 27

d. 15

14.

Reduce to lowest terms.

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15.

Simplify and express your answer using positive exponents only..0/msohtmlclip1/01/clip_image031.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/75133e40-b573-4aed-872d-739f93f21e2b.gif”>

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16.

Evaluate. (–2)–2

a.1/4

b. 1

c. 2

d. 4

17.

Change to rational exponent form. Do not simplify. .0/msohtmlclip1/01/clip_image036.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/0a29fe3e-2d35-437f-ad78-4111c32e7872.gif”>

a.1601/2

b.1602

c.21601

d. 2

18.

Perform the indicated operations and reduce to lowest terms.

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d.1

19.

Factor completely, relative to the integers. 49a2b – b3

a.(7a + b2)(7a – b)

b. b(7a + b)(7a – b)

c.b(7a – b)2

d. Prime, doesn’t factor

20.

Evaluate the expression if it is a real number. .0/msohtmlclip1/01/clip_image041.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/871adfad-4b19-4ab5-a11f-da8aaa25d199.gif”>

a. –12

b. 3

c. –3

d. Not a real number

21.

Perform the indicated operations and simplify. 5x – 4x[8 – 3(x – 2)]

a.6×2 – 3x

b.12×2 – 51x

c.12×2 + 5x + 6

d.12×2 + 5x – 6

22.

Evaluate..0/msohtmlclip1/01/clip_image042.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/6d2afd5d-5b8a-497e-9b46-293f4e40e09c.gif”>

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c. 2

d. –2

23.

Evaluate the expression if it is a real number. .0/msohtmlclip1/01/clip_image044.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/3c8d0658-55df-459f-8464-ba852e501f75.gif”>

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c.-16

d. Not a real number

24.

Factor completely, relative to the integers. 9×2 + 12x + 4

a.(3x + 2)2

b. (3x – 2)(3x + 2)

c. (9x + 2)(x + 2)

d. (3x + 1 )(3x + 4)

25.

Change to radical form. Do not simplify..0/msohtmlclip1/01/clip_image046.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/ec492b55-276a-405d-be3f-707eb40cb99d.gif”>

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26.

Change to radical form. Do not simplify..0/msohtmlclip1/01/clip_image051.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/93c31122-a1bb-4131-925b-3f957bb7b498.gif”>

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27.

Write the expression in simplified radical form. .0/msohtmlclip1/01/clip_image056.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/a336881a-9380-4fb1-92c0-bf7de585db54.gif”>

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28.

Perform the indicated operations and simplify. (5x – 3y)2

a.25×2 – 30xy + 9y2

b.25×2 – 9y2

c.25×2 – 30xy – 9y2

d.25×2 + 9y2

29.

Change to rational exponent form. Do not simplify. .0/msohtmlclip1/01/clip_image061.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/839ae805-d9a8-421b-8fea-fdbd6ec9a6bc.gif”>

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30.

Factor completely, relative to the integers. x2 + 36

a. (x – 6)(x + 6)

b. (x + 1)(x + 36)

c.(x + 6)2

d. Prime

31.

Add 2×2 – 8x – 5 and 5×2 – 4x – 10.

a.7×2 – 12x – 15

b.7×2 – 12x + 5

c.7×2 + 4x – 15

d.7×2 + 4x + 5

32.

Simplify and express your answer using positive exponents only.

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33.

Write the expression in simplified radical form. .0/msohtmlclip1/01/clip_image071.gif” alt=”Description: http://student.allied.edu/uploadedfiles/images/215861e1-a3a5-46c6-9701-c06741f0aaea.gif”>

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34.

Perform the indicated operations and reduce to lowest form. Represent any compound fractions as simple fractions reduced to lowest terms.

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vv

week 2

Adjust Value: 0.00
Feedback

Question Points

1. Graph the inequality on a real number line. –4 < x –3

b. x < –3

c. x –3

1

5. Solve. 6x + 6 = 2x – 10

a. –5

b. –4

c. –3

d. –2

1

6. Solve. Write the answer in interval notation. |12 – 5x| 9

b. |x – 5| > 9

c. |x + 5| > 9

d. |x + 5| > 9

1

8. Solve. 5(x + 9) + 7x = 8x + 1

a. –11

b. 5

c. 11

d. -9

.

1

9. Write as a single interval, if possible. (–2, 4] [0, 5)

a. (–2, 5)

b. [0, 4]

c. (–2, 4]

d. [0, 5)

.

1

10. Solve. 4(x – 2) + 6x = 12

a.

b.

c. 1

d. 2

1

11. Solve.

a. (-?, -75] [-15, ?)

b. (-?, 15] [75, ?)

c. [-75, -15]

d. [15, 75]

\

1

12. Solve and graph. 0.8(x + 9) > 0.5x + 6.3

a.

b.

c.

d.

1

13. Solve and graph. 3x + 6 > x + 8

a.

b.

c.

d.

1

14. Solve. |x + 12| = 2x + 1

a. 11

b. –

c. 11, –

d. 11,

0

15. Solve. |x – 2| = 7

a. 9, 5

b. 9, –5

c. –9, –5

d. –9, 5

1

16. Solve. Write the solution in interval notation. |x + 10| > 3

a. (–?, –13) (–7, ?)

b. (–?, –13] [–7, ?)

c. (–13, –7)

d. [–13, –7]

1

17. A musician is planning to market a CD. The fixed costs are $560 and the variable costs are $4 per CD. The wholesale price of the CD will be $8. For the artist to make a profit, revenues must be greater than costs. How many CDs, x, must be sold for the musician to break even?

a. x = 170

b. x = 140

c. x = 190

d. x = 200

LO2E:Write and solve a single variable linear equation or inequality to solve a real-world problem.

1

18. Solve.

a. –5

b. 5

c. 2

d. No solution

LO2A:Solve single-variable linear equations.

1

19. Solve and graph. –3x > 3

a.

b.

c.

d.

1

20. How much pure antifreeze must be added to 12 gallons of 20% antifreeze to make a 40% antifreeze solution?

a. 2 gallons

b. 4 gallons

c. 6 gallons

d. 8 gallons

1

Solve by completing the squ
are. x2 + 10x + 19 = 0
a. ±31

b.

c.

d. -5

1

2. Solve by using the square root property. (x – 1)2 = 5

a.

b. -1

c.

d. -1i

3.

When a stone is dropped into a deep well, the number of seconds until the sound of a splash is heard is given by the formula,

where x is the depth of the well in feet. For one particular well, the splash is heard 17 seconds after the stone is released. How deep (to the nearest foot) is the well?

a. 761 ft

b. 1,339 ft

c. 3,140 ft

d. 4,463 ft

4. Solve.

a. 0, –

b. 0,

c. 0

d. No solution

5. Solve. 9×2 = –5x

a. –

b. –

c. –

d. –

1

6. A speedboat takes 3 hours longer to go 60 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?

a. 3 mi/h

b. 4 mi/h

c. 5 mi/h

d. 6 mi/h

1

7. Solve by completing the square. x2 – 6x – 2 = 0

a.

b. –

c.

d. –

1

8. Solve the equation. 6x-2/5 + 3x-1/5 – 1 = 0

a.

b.

c.

d.

0

9. Two trains travel at right angles to each other after leaving the same train station at the same time. One hour later they are 100 miles apart. If one travels 20 miles per hour faster than the other, what is the rate of the faster train?

a. 60 mph

b. 70 mph

c. 80 mph

d. 90 mph

10. Solve by factoring. 3×2 = –18x

a. 0, –6

b. 0, 6

c. 6, –6

d. 2, 6

Hint: Sections 1.5-1.6

SLO3:Solve quadratic equations by factoring, using the square root property, completing the square, or by quadratic formula.

LO3A:Solve quadratic equations by factoring, by square root property, completing the square, or by quadratic formula.

1

mod 4

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. Sketch the graph of the equation. xy = 4

a.

Symmetric with respect to the origin.

b.

Symmetric with respect to the origin.

c.

Symmetric with respect to the x-axis.

d.

Symmetric with respect to the y-axis.

2. Indicate the slope. 3x + 4y = 12

a. –

b.

c. –

d.

e.

Indicate the slope. 3x + 4y = 12

a. –

b.

c. –

d.

Indicate the slope, if it exists. y = –3

a. 3

b. 0

c. -3

d. Undefined

.

1

4. Write the equation of the line which passes through (2, –1) and is perpendicular to the line with equation 3y – x = 1.

a. 3x + y = 5

b. 3x – y = 7

c. x + 3y = –1

d. x – 3y = 5

Hint:Sections 2.1-2.3

M is the midpoint of A and B. Find the indicated point. Verify that

a. (0.9, –4.7)

b. (–6.1, –5.7)

c. (6.1, 5.7)

d. (–27.1, –8.7)

Write the equation of the line passing through (–3, –5) and (3, 0). Write your answer in the slope-intercept form y = mx + b.

a.

b.

c.

d.

Hint:Sections 2.1-2.3

Write the equation of the line which passes through (2, –1) and is perpendicular to the line with equation 3y – x = 1.

a. 3x + y = 5

b. 3x – y = 7

c. x + 3y = –1

d. x – 3y = 5

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. x2 + y2 + x2y2 = 4

a. Symmetric with respect to the x-axis

b. Symmetric with respect to the y-axis

c. Symmetric with respect to the origin

d. Symmetric with respect to the x-axis, the y-axis, and the origin

Reflect A, B, C, and D through the x-axis and then through the y-axis and give the coordinates of the reflected points, A’, B’, C’, and D’.

a. A’ = (–1, 0), B’ = (–3, 6), C’ = (3, 1), D’ = (2, –5)

b. A’ = (0, –1), B’ = (–6, –3), C’ = (1, 3), D’ = (5, 2)

c. A’ = (0, –1), B’ = (6, –3), C’ = (1, 3), D’ = (–5, 2)

d. A’ = (1, 0), B’ = (3, –6), C’ = (–3, –1), D’ = (–2, 5)

?

Reflect A, B, C, and D through the y-axis and give the coordinates of the reflected points, A’, B’, C’, and D’.

a. A’ = (–1, 0), B’ = (–3, –6), C’ = (3, –1), D’ = (2, 5)

b. A’ = (0, 1), B’ = (6, 3), C’ = (1, –3), D’ = (–5, –2)

c. A’ = (0, –1), B’ = (–6, –3), C’ = (–1, 3), D’ = (5, 2)

d. A’ = (1, 0), B’ = (3, –6), C’ = (–3, 1), D’ = (2, –5)

Solve for y, producing two equations, and then graph both of these equations in the same viewing window.

(y – 2)2 – x2 = 9

a.

b.

c.

d.

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. x2 + 6xy + y2 = 1

a. Symmetric with respect to the x-axis

b. Symmetric with respect to the y-axis

c. Symmetric with respect to the origin

d. Symmetric with respect to the x-axis, the y-axis, and the origin

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. x2y + 4y2 = 1

a. Symmetric with respect to the x-axis

b. Symmetric with respect to the y-axis

c. Symmetric with respect to the origin

d. Not symmetric with respect to the x-axis, the y-axis, or the origin

?

Find the distance between (–3, –2) and (1, 4).

a. 27

b.

c.

d.

LO4B:Calculate the distance between two points.

a. x = –2

b. y = –2

c. y = x – 2

d. y = 2x

?

. Reflect A, B, C, and D through the origin and give the coordinates of the reflected points, A’, B’, C’, and D’.

a. A’ = (–1, 0), B’ = (–3, 6), C’ = (3, 1), D’ = (2, –5)

b. A’ = (0, –1), B’ = (–6, –3), C’ = (1, 3), D’ = (5, 2)

c. A’ = (1, 0), B’ = (3, –6), C’ = (–3, –1), D’ = (–2, 5)

d. A’ = (0, –1), B’ = (6, –3), C’ = (1, 3), D’ = (–5, 2)

Write the equation of the line with slope 0 and y-intercept –3. Write the equation in standard form Ax + By = C, A > 0.

a. –3x – y = 0

b. –3x + y = 0

c. y = –3

d. -3

Write an equation of the line passing through (–8, –3) and perpendicular to y = . Write your answer in standard form Ax + By = C, A > 0.

a. 4x + y = –35

b. 4x – y = –35

c. x + 4y = –20

d. x – 4y = –20

. Indicate the slope. 3x + 2y = 6

a.

b. –

c.

d. –

LO4D:Det

?

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. Sketch the graph of the equation. y2/7 = x

a.

Symmetric with respect to the y-axis.

b.

Symmetric with respect to the x-axis.

c.

Symmetric with respect to the y-axis.

d.

Symmetric with respect to the x-axis.

.

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. y = x – 3

a. Symmetric with respect to the x-axis

b. Symmetric with respect to the y-axis

c. Symmetric with respect to the origin

d. No symmetry with respect to x-axis, y-axis, or origin

mod 5

mod 5

Find the intervals over which f is increasing.

a. (–?, –2], [1, ?)

b. (–3, ?)

c. (–?, –3], [1, ?)

d. None

The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.

a.

b.

c.

d.

Hint: Sections 3.1-3.3

Indicate whether the table defines a function.

a. Function

b. Not a function

Hint: Sections 3.1-3.3

?

Determine whether the function is even, odd, or neither. f(x) = x5 + 4

a. Even

b. Odd

c. Neither

Hint: Sections 3.1-3.3

Determine the function represented by the graph.

a. f(x) = |x + 3| + 1

b. f(x) = |x – 3| + 1

c. f(x) = |x + 1| + 3

d. f(x) = |x – 1| + 3

Hint:Sections 3.1-3.3

Use the graph of the function to estimate: (a) f(1), (b) f(–5),and (c) All x such that f(x) = 3

a. (a) –3 (b) –9 (c) 7

b. (a) –3 (b) –9 (c) –1

c. (a) 5 (b) –1 (c) 7

d. (a) 5 (b) –1 (c) –1

Hint: Sections 3.1-3.3

?

Find the .homeworkminutes.com/question/view/126947/allied-mat120-module-5-check-your-understanding-latest-2015#”>domain of f.

a. (–?, ?)

b. (–?, –3) (1, ?)

c. (–?, –2) (–2, ?)

d. (–?, –2) (1, ?)

?

raph f(x) = |x – 1|.

a.

b.

c.

d.

Hint:Sections 3.1-3.3

SLO4:Graph functions, analyze graphs, perform operations on functions, and determine if functions are one-to-one.

LO4J:Graph functions.

LO4M:Perform operations on functions.

The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of f(x) = is shifted two units to the left and five units down.

a.

b.

c.

d.

Hint: Sections 3.1-3.3

Evaluate f(11).

a. 11

b. 7

c. 12

d. –2

Hint: Sections 3.1-3.3

ndicate whether the table defines a function.

a. Function

b. Not a function

Hint: Sections 3.1-3.3

Graph h(x) = f(x) – 2.

a.

b.

c.

d.

Hint: Sections 3.1-3.3

Use the graph of the function to estimate: (a) f(–6), (b) f(1), (c) All x such that f(x) = 3

a. (a) 4 (b) 3 (c) –5, 1

b. (a) 5 (b) 4 (c) –3, 1

c. (a) 1 (b) 2 (c) –5, 2

d. (a) 7 (b) 5 (c) –5, 6

Hint: Sections 3.1-3.3

Indicate whether the set defines a function. If it does, state the domain and range of the function. {(9, 5), (10, 5), (11, 5), (12, 5)}

a. A function; Domain = {5}; Range = {5}

b. A function; Domain = {5}; Range = {9, 10, 11, 12}

c. A function; Domain = {9, 10, 11, 12}; Range = {5}

d. Not a function

Hint: Sections 3.1-3.3

raph y = (x – 2)2 + 1

a.

b.

c.

d.

Indicate whether the graph is the graph of a function.

a. Function

b. Not a function

Hint: Sections 3.1-3.3

Evaluate f(–10).

a. –10

b. 8

c. –9

d. –3

Hint:Sections 3.1-

Find the range of f.

a. (–?, ?)

b. (–?, –3] (1, ?)

c. (–?, –3] [1, ?)

d. (–?, –3) (1, ?)

Hint: Sections 3.1-3.3

SLO4:Graph func

Find the domain of f.

a. {x | x 3, 5}

b. {x | x 3}

c. {x | x 5}

d. All real numbers

?

Find the domain of the function. Express your answer in interval notation.

a.

b.

c.

d.

Hint: Sections 3.1-3.3

Indicate whether the graph is the graph of a function.

a. Function

b. Not a function

Hint: Sections 3.1-3.

Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y. x|y| = x + 5

a. A function with domain all real numbers

b. A function with domain all real numbers except 0

c. Not a function: when x = 0, y = ±5

d. Not a function: when x = 1, y = ±6

Hint: Sections 3.1-3.3

Find the y-intercept.

a.

b. –

c. –1

d. None

?

Graph h(x) = f(x – 2).

a.

b.

c.

d.

Hint:Sections 3.1-3.3

Find the value of f(3) if f(x) = 4×2 + x.

a. 38

b. 39

c. 40

d. 41

Hint: Sections 3.1-3.3

?

Find the intervals over which f is constant.

a. (–3, 1)

b. (–3, 1]

c. (–2, 1]

d. None

?

Evaluate f(3).

a. 3

b. 2

c. 4

d. 5

?

Find the x-intercept.

a. –

b. 3

c. 2

d. None

Find the x-intercept(s).

a. –2

b. 1, –3

c. –3

d. None

?

Determine whether the function is even, odd, or neither. f(x) = x4 + 3×2

a. Even

b. Odd

c. Neither

Hint: Sections 3.1-3.3

mod 6

Find (f + g)(–3). and

a. 0

b. 1

c. 2

d. Undefined

Hint: Sections 3.4-3.6

?

?

Find the vertex and axis of the parabola, then draw the graph.

a.

Vertex: (–2, –5); axis: x = –2

b.

Vertex: (2, –5); axis: x = 2

c.

Vertex: (2, 5); axis: x = 2

d.

Vertex: (2, 5); axis: x = 2

Hint: Sections 3.4-3.6

SLO5:Graph quadratic and inverse functions.

LO5A:Solve and graph quadratic functions.

Which of the following is a brief verbal description of the relationship between the graph of the indicated function and the graph of y = x2?

a. The graph is shifted 4 units left and 7 units down.

b. The graph is shifted 7 units right and 4 units down.

c. The graph is shifted 4 units right and 7 units down.

d. The graph is shifted 7 units left and 4 units down.

Hint: Sections 3.4-3.6

Sketch the graph. f(x) = x2 – 4x + 3

a.

b.

c.

d.

Hint: Sections 3.4-3.6

Find the axis of symmetry. f(x) = x2 + 8x – 9

a. x = –4

b. x = 4

c. x = –8

d. x = 8

?

Sketch the graph. f(x) = x2 – 4x + 5

a.

b.

c.

d.

Hint: Sections 3.4-3.6

Find the inverse function f–1. Then graph both functions on the same set of axes. f(x) = 2x – 4

a.

b.

c.

d.

Hint: Sections 3.4-3.6

Determine whether the function is one-to-one.

a. One-to-one

b. Not one-to-one

Determine whether the function is one-to-one.

a. One-to-one

b. Not one-to-one

Determine whether the function is one-to-one.

a. One-to-one

b. Not one-to-one

Hint: Sections 3.4-3.6

Which of the following is a brief verbal description of the relationship between the graph of the indicated function and the graph of y = x2?

a. The graph is shifted 4 units to the right and 6 units up.

b. The graph is shifted 4 units to the right and 6 units down.

c. The graph is shifted 4 units to the left and 6 units down.

d. The graph is shifted 4 units to the left and 6 units up.

Hint: Sections 3.4-3.6

SLO4:Graph functions, analyze graphs, perf

ind (f + g)(–3).

a. 0

b. 1

c. 2

d. 3

Find h(x) = (g f)(x). f(x) = and g(x) = 3x – 5

a. h(x) =

b. h(x) =

c. h(x) =

d. h(x) =

Hint:Sections 3.4-3.6

Determine whether the function is one-to-one. {(4, –4), (2, –1), (9, –5), (0, –2), (3, –3)}

a. One-to-one

b. Not one-to-one

Hint: Sections 3.4-3.6

etermine whether the function is one-to-one. f(x) = –2x – 1

a. One-to-one

b. Not one-to-one

Find h(x) = (f g)(x). f(x) = and g(x) = 3x – 5

a. h(x) =

b. h(x) =

c. h(x) =

d. h(x) =

Determine if g is the inverse of f. f(x) = x3 + 5 g(x) =

a. Yes

b. No

Hint: Sections 3.4-3.6

ind (f g)(1). and

a. 0

b. 1

c. 2

d. Undefined

Match the graph to its equation.

a. f(x) = (x – 1)2 + 4

b. f(x) = (x – 1)2 – 4

c. f(x) = (x + 1)2 + 4

d. f(x) = (x + 1)2 – 4

Hint: Sections 3.4-3.6

Find the inverse function f-1. f(x) = 6 +

a. f-1(x) =

b. f-1(x) =

c. f-1(x) =

d. f-1(x) =

Hint: Sections 3.4-3.6

Graph f(x) = x2 – 2x – 3.

a.

b.

c.

d.

Hint: Sections 3.4-3.6

?

ind (–2)

a. 0

b. 1

c. 2

d. 3

Determine if g is the inverse of f. f(x) = 3x – 1 g(x) =

a. Yes

b. No

Hint: Sections 3.4-3.6

SLO5:Graph quadratic and inverse functions.

LO5C:Find the inverse of a function.

1

24. Determine whether the function is one-to-one. f(x) = 7×2 + 8

a. One-to-one

b. Not one-to-one

Hint: Sections 3.4-3.6

Determine whether the function is one-to-one. f(x) = 7×2 + 8

a. One-to-one

b. Not one-to-one

Hint: Sections 3.4-3.6

?

ind the inverse function f-1. f(x) = 3x + 8

a.

b.

c.

d.

V

?

Find the vertex and axis of the parabola, then draw the graph.

a.

Vertex: (12, 10); axis: x = 12

b.

Vertex: (12, 10); axis: x = 12

c.

Vertex: (–12, 10); axis: x = –12

d.

Vertex: (–12, 10); axis: x = –12

Hint: Sections 3.4-3.6

?

?

Graph f(x) = –x2 + 6x – 5.

a.

b.

c.

d.

Hint: Sections 3.4-3.6

Find f + g. f(x) = and g(x) =

a. (f + g)(x) =

b. (f + g)(x) =

c. (f + g)(x) =

d. (f + g)(x) =

Find fg. f(x) = and g(x) =

a. (fg)(x) =

b. (fg)(x) =

c. (fg)(x) =

d. (fg)(x) =

etermine whether the function is one-to-one. {(–1, –4), (–3, –1), (4, –5), (–5, –4), (–2, –3)}

a. One-to-one

b. Not one-to-one

Hint: Sections 3.4-3.6

SLO4:Graph functions, analyze graphs, perform operations on functions, and determine if functions are one-to-one.

ind (g f)(–6).

a. –3

b. 3

c. 2

d. –2

ind the coordinates of the vertex. f(x) = x2 – 4x + 5

a. (2, 1)

b. (–2, 1)

c. (–1, 2)

d. (–1, –2)

Hint: Sections 3.4-3.6

SLO5:Graph quadratic and inverse functions.

Find the standard form of the equation for the quadratic function whose graph is shown.

a. f(x) = –x2 + 6x – 5

b. f(x) = –x2 – 6x – 5

c. f(x) = –x2 + 3x – 5

d. f(x) = –x2 – 3x – 5

Find the standard form of the equation for the quadratic function whose graph is shown.

a. f(x) = –x2 + 6x – 5

b. f(x) = –x2 – 6x – 5

c. f(x) = –x2 + 3x – 5

d. f(x) = –x2 – 3x – 5

ind (f – g)(2).

a. –4

b. –1

c. 0

d. –2

Hint: Sections 3.4-3.6

SLO4:Graph functions, analyze graphs, perform operations on functions, and determine if functions are one-to-one.

mod 7

The bacteria in a certain culture double every 7.9 hours. The culture has 2,000 bacteria at the start. How many bacteria will the culture contain after 4 hours?

a. 3,306 bacteria

b. 3,409 bacteria

c. 3,508 bacteria

d. 3,628 bacteria

If you invest $4,500 in an account paying 2% compounded continuously, how much money will be in the account at the end of 4 years?

a. $4,874.79

b. $4,879.93

c. $4,884.77

d. $4,888.11

Simplify. log 2 27

a. 0

b. 1

c. 2

d. 7

?

Evaluate x to four significant digits. ln x = –1.445

a. 0.2357

b. 0.2711

c. 0.3589

d. 0.4513

Given that log x = 6 and log y = 5, find log ( ).

a. 180

b. 4,500

c. 27

d. 161

a. 3

b. 4

c. 5

d. –4

Simplify. log 4 1

a. 0

b. 1

c. 4

d. 16

Simplify. log 3 3

a. 0

b. 1

c. 3

d. 9

Write in logarithmic form. 243 = 35

a. log 3 5 = 243

b. log 5 3 = 243

c. log 3 243 = 5

d. log 243 3 = 5

Simplify.

a. 0

b. 1

c. 4

d. 7

Write in exponential form. log 10 0.0001 = –4

a. 0.0001 = 10–4

b. 0.0001 = (–4)10

c. 10 = (0.0001)–4

d. 10 = (–4)0.0001

Use a calculator to find log 5 57. Round your answer to four decimal places.

a. 2.3611

b. 2.5001

c. 2.5121

d. 2.8251

Solve. x2ex + 4xex = 0

a. 0

b. –4

c. 0, 4

d. 0, –4

Hint: Sections 5.1, 5.3

The population of a certain geographic region is approximately 111 million and grows continuously at a relative growth rate of 1.17%. What will the population be in 8 years? Compute the answer to three significant digits.

a. 121 million people

b. 122 million people

c. 123 million people

d. 124 million people

plify.

a.

b.

c.

d.

Simplify. log 2

a.

b. –

c. 5

d. –5

?

An employee is hired to assemble toys. The learning curve

gives the number of toys the average employee is able to assemble per day after t days on the job. How many toys can the average employee assemble per day after 6 days of training? Round to the nearest integer.

a. 24 toys

b. 25 toys

c. 26 toys

d. 27 toys

Simplify.

a. 0

b. 27

c.

d.

Hint: Sections 5.1, 5.3

Graph the logarithmic function. f(x) = log 3 (x – 1)

a.

b.

c.

d.

Graph y = ex – 2.

a.

b.

c.

d.

mod 8

A mail-order garden equipment business shipped 120 packages one day. Customers were charged $3.50 for each standard-delivery package and $7.50 for each express-delivery package. Total shipping charges for the day were $596. How many of each kind of packages were shipped?

a. 76 standard packages; 44 express packages

b. 44 standard packages; 76 express packages

c. 66 standard packages; 54 express packages

d. 54 standard packages; 66 express packages

Hint: Sections 7.1

dult tickets for a play cost $8 and child tickets cost $6. If there were 20 people at a performance and the theatre collected $152 from ticket sales, how many adults and how many children attended the play?

a. 16 adults and 4 children

b. 4 adults and 16 children

c. 9 adults and 11 children

d. 11 adults and 9 children

?

order to get 10 pound mixture worth $8.40 per pound. How much of each type of coffee was used?

a. 4 lb French roast; 6 lb Kenyan

b. 6 lb French roast; 4 lb Kenyan

c. 3 lb French roast; 7 lb Kenyan

d. 7 lb French roast; 3 lb Kenyan

olve the system of equations by using the elimination method.

x+y=9

2x-3y=-2

a. (4, 5)

b. (9, 1)

c. (9, 0)

d. (5, 4)

Solve the system using the substitution method.

y = 3x + 2

3x – y = -3

a. (0, 0)

b. (0, 2)

c. (1, 5)

d. no solution

Solve the system of equations by using the elimination method.

x + y = 4

x – y = 2

a. (1, 3)

b. (–1, 5)

c. (3, 1)

d. (5, –1)

Solve the system by the substitution method.

4x + 3y = 5

6x + y = -1

a.

b.

c.

d.

?

olve the system using the substitution method.

7x – 2y = 5

6x + 5y = 11

a. (2, 1)

b. (1, 2)

c. (-1, 1)

d. (1, 1)

Janet invested $10,000, part at 2% and part at 12%. If the total interest at the end of the year is $600, how much did she invest at 2%?

a. $4,000

b. $7,000

c. $6,000

d. $5,000

Hint: Sections 7.1

SLO7:Solve systems of equations.

LO7C:Write and solve systems of equations to solve real-world problems.

Solve the system of equations by the elimination method.

x – y = 4

x + 2y = –14

a. (–2, –6)

b. (–3, –6)

c. (–2, –5)

d. (–3, –5)

homeworks

week 1

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter R.

· Section R-1 (pages 9-10) #2, 8, 22, 26

· Section R-2 (pages 20-21) #28, 34, 40, 44, 56, 62, 66, 82

· Section R-3 (pages 29-30) #1-4, 16-20 even, 24, 28, 44, 50, 56

· Section R-4 (pages 37-38) #8, 10, 24, 34

R

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter 1: Section Exercises.

Section 1.5 Exercises (pp. 94-96):
Problems: 7, 9, 11, 13, 16, 18, 19, 21, 24, 28, 30, 31, 33, 34, 40, 81, 97
Section 1.6 Exercises (p. 103):
Problems: 13-23 odd, 27

mod 2

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter 1: Section Exercises.

Note:Disregard any directions to graph on a number line.

Section 1.1 Exercises (p. 54-56):
Problems: 9-25 odd, 35, 39-45 odd, 61, 71, 83
Section 1.2 Exercises (p. 62-64):
Problems: 17, 19, 29-39 odd, 43-53 odd, 89, 91
Section 1.3 Exercises (p. 73):
Problems: 31-53 odd

homework 4

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter 2: Section Exercises.

Section 2.1 Exercises (p. 120):
Problems: 37-45 odd
Section 2.2 Exercises (p. 130):
Problems: 5-11 odd
Section 2.3 Exercises (p. 144-145):
Problems: 7-65 odd

mod 5

Running head: [INSERT TITLE HERE]

[INSERT TITLE HERE]

Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter 3: Section Exercises.

Section 3.1 Exercises (pp. 171-173):
Problems: 7-51 odd

mod 6

Running head: [INSERT TITLE HERE]

[INSERT TITLE HERE]

Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter 3: Section Exercises.

Note:Disregard any directions that ask to draw a graph.

Section 3.4 Exercises (p. 217-218):
Problems: 19-27 odd, 83, 85, 89
Section 3.5 Exercises (p. 232-233):
Problems: 11-33 odd, 43-53 odd, 61, 63
Section 3.6 Exercises (p. 247-248):
Problems: 7-39 odd

mod 7

Directions: Show your work on all of these problems. You may find Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

Complete the following problems in Chapter 5: Section Exercises.

Section 5.1 Exercises (pp. 337-339):
Problems: 5-15 odd, 33-49 odd, 87, 89, 99
Section 5.3 Exercises (pp. 363-364):
Problems: 7-17 odd, 23-77 odd
Chapter 5 Review Exercises (page 380)
Problem: 1

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