Choose the one alternative that best completes the statement

| August 30, 2017

Question
Math 010 Exam 4

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
5x
1) f(x) =
4+x
A) {x|x is a real number and x
C) {x|x is a real number and x

1)
0}
0, x

B) {x|x is a real number and x
D) {x|x is a real number and x

-4}

4}
-4}

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the rational expression.
4x – 24
2)
6-x

2)

Multiply or divide as indicated. Simplify completely.
3x – 3
4×2
·
3)
x
7x – 7

4)

3)

x2 – 8x + 16 3x – 12
÷
11x – 44
33

4)

Solve the problem.
5) A publishing company estimates the revenue from the sale of a popular book by the
900×2
rational function R(x) =
where x is the number of years since publication and R(x) is
x2 + 6

5)

the total revenue in millions of dollars. Find the total revenue at the end of the second
year.

Perform the indicated operation. Simplify if possible.
x
6
+
6)
x-8 x-8

6)

Find the LCD of the rational expressions in the list.
1
3
,
7)
8a a 2 + 4a

7)

Perform the indicated operation. Simplify if possible.
2
6
8) +
r r- 8

8)

1

Divide.

-24×2 – 20x – 12
4

9)

10) (x2 – 4x – 5) ÷ (x + 1)

10)

9)

Solve the equation for the specified variable.
Fd
for t
11) P =
t

11)

Solve the equation.
x
9 x-6
– =
12)
14 7
7

Solve.

12)

13) A recent advertisement claimed that 2 out of every 3 doctors recommend a certain herbal
supplement to increase energy levels. If a local hospital employs 220 doctors, how many
doctors would you expect to recommend the supplement? (Round to the nearest whole
number, if necessary.)

13)

Write an equation to describe the variation. Use k for the constant of proportionality.
14) s varies directly as m

14)

If y varies directly as x, find the direct variation equation for the situation.
15) y = 12 when x = 20

15)

Write an equation to describe the variation. Use k for the constant of proportionality.
16) a varies inversely as y

16)

If y varies inversely as x, find the inverse variation equation for the situation.
17) y = 7 when x = 2

17)

2

Fill in the blank with one of the words or phrases listed below.
rational expression
equation
long division
expression
least common denominator

18) A(n)

complex fraction
jointly

opposites
directly

is an expression that can be written as the quotient

synthetic division
inversely

P
of two
Q

18)

polynomials P and Q as long as Q is not 0.

19) Which is an expression and which is an equation? An example of a(n)
2

x2

= 7 and an example of a(n)

is

is

2
+
x

19)

2
5
+
.
x x2

20) A rational expression whose numerator, denominator, or both contain one or more rational
expressions is called a
.

3

20)

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D
-4
12x/7
1
360
(x+6)/(x-8)
8a(a+4) = 8a2 + 32a
[2(r-8) + 6r] /[r(r-8)] = (8r – 16)/[r(r – 8)]
-6×2 – 5x – 3
x–5
t…

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