Chapter 7 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Rationalize the denominator of the expression. Assume that all variables are positive.
____
____
____
____
____
____
1.
a.
c.
b.
d.
a.
c.
b.
d. none of these
a.
c.
b.
d.
2.
3.
4. Solve
a. 3, –4
b. 3, –3
.
5. Find all the real square roots of
c. no solution
d. 3, –3, 4, –4
.
a. no real root
c.
b.
d.
6. Multiply and simplify
a.
b.
and
. Assume that all variables are positive.
c.
d. none of these
____
____
____
7. Write the exponential expression
a.
b.
8. Write the radical expression
in radical form.
c.
d.
in exponential form.
a.
b.
c.
9. Write
a.
in simplest form.
d.
c.
b.
d. none of these
Solve the equation.
____ 10.
a. 11; –11
b. 7
d. 5; –11
c. 1
Solve. Check for extraneous solutions.
____ 11.
a.
b.
4
2
and 
5
5
____ 12. Let
a. 2x – 4
____ 13. Let
a. 2x – 5
and
b. –8x – 8
and
b. 2x + 5
____ 14. Let
a.
b.
____ 15. Let
a.
b.
c.
d.
____ 16. Let
c.
4
5
2
5
. Find f(x) + g(x).
c. –8x – 4
. Find f(x) – g(x).
c. 4x – 1
. Find 2f(x) – 3g(x).
c.
d.
and
and

. Find
and its domain.
; all real numbers except x  
2
3
; all real numbers
; all real numbers
; all real numbers except x  
and
a. 3; all real numbers
b. 3; all real numbers except x  2
c. 1; all real numbers
. Find
6
7
and its domain.
d.

4
5
d. 2x – 8
d. 2x – 1
d. –3; all real numbers except x  3
____ 17. Let
and
. Find
and its domain.
3x + 2; all real numbers except x  4
–9x + 6; all real numbers except x  4
–3x + 2; all real numbers except x  –4
9x – 6; all real numbers except x  –4
a.
b.
c.
d.
____ 18. Let
a. 23
and
b. –53
____ 19. Let
. Find
c. –9
and
a.
.
. Find
b.
d. 3
.
c.
d.
____ 20. Let
and
. Find f(g(x)) and g(f(x)).
a. f(g(x)) = 10x – 1; g(f(x)) = 10x + 7
b. f(g(x)) = 7x + 3; g(f(x)) = 10x + 7
c. f(g(x)) = –7x – 3; g(f(x)) = –10x + 7
d. f(g(x)) = –10x – 7; g(f(x)) = 7x + 3
____ 21. Graph the relation and its inverse. Use open circles to graph the points of the inverse.
x
0
4
9
10
y
3
2
7
–1
a.
c.
y
–8
y
8
8
4
4
–4
4
8
x
–8
–4
4
–4
–4
–8
–8
8
x
b.
d.
y
–8
y
8
8
4
4
–4
4
8
–8
x
–4
–4
–4
–8
–8
____ 22. Find the inverse of
a.
4
8
x
2
4
x
.
c.
b.
d.
____ 23. Graph
a.
and its inverse.
c.
y
–4
y
4
4
2
2
–2
2
4
x
–4
–2
–2
–2
–4
–4
b.
d.
y
–4
y
4
4
2
2
–2
2
4
–4
x
–2
2
–2
–2
–4
–4
____ 24. For the function
a.
, find
;
. Determine whether
4
x
4
x
is a function.
is not a function.
b.
;
is not a function.
c.
;
is a function.
d.
;
____ 25. For the function
a. 14
is a function.
, find
.
c. –5
b. 5
d. 25
Graph the function.
____ 26.
a.
c.
y
–4
y
4
4
2
2
–2
2
4
x
–4
–2
2
–2
–2
–4
–4
b.
d.
y
–4
y
4
4
2
2
–2
2
4
–4
x
–2
–2
–2
–4
–4
2
4
x
2
4
x
2
4
x
____ 27.
a.
–4
4
2
2
–2
2
4
–4
x
–2
–2
–2
–4
–4
d.
y
–4
y
4
b.
____ 28.
c.
y
y
4
4
2
2
–2
2
4
x
–4
–2
–2
–2
–4
–4
a.
c.
y
–8
8
8
4
4
–4
4
8
–8
x
–4
–4
–4
–8
–8
b.
d.
y
–8
y
8
4
4
4
8
–8
x
8
x
4
8
x
4
8
x
y
8
–4
4
–4
–4
–4
–8
–8
____ 29.
a.
c.
y
–8
y
8
8
4
4
–4
4
8
x
–8
–4
–4
–4
–8
–8
b.
d.
y
–8
8
8
4
4
–4
4
8
–8
x
4
–4
–8
–8
y
2
4
–4
–4
____ 30. Which function matches the graph?
2
y
6
8
10 x
–2
–4
–6
a.
c.
b.
d.
8
x
Chapter 7 Test
Answer Section
MULTIPLE CHOICE
1. ANS: D
PTS: 1
DIF: L3
REF: 7-3 Binomial Radical Expressions
OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
STA: CA A2 15.0 TOP: 7-3 Example 6
KEY: binomial radical expressions | multiplying binomial radical expressions | rationalize the denominator
2. ANS: A
PTS: 1
DIF: L3
REF: 7-2 Multiplying and Dividing Radical Expressions
OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 5
KEY: divide radical expressions | simplifying a radical expression
3. ANS: C
PTS: 1
DIF: L2
REF: 7-3 Binomial Radical Expressions
OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
STA: CA A2 15.0 TOP: 7-3 Example 6
KEY: binomial radical expressions | conjugates | multiplying binomial radical expressions | simplifying a
radical expression
4. ANS: D
PTS: 1
DIF: L2
REF: 6-4 Solving Polynomial Equations
OBJ: 6-4.2 Solving Equations by Factoring
STA: CA A2 4.0
TOP: 6-4 Example 6
KEY: factoring a polynomial | polynomial
5. ANS: A
PTS: 1
DIF: L2
REF: 7-1 Roots and Radical Expressions
OBJ: 7-1.1 Roots and Radical Expressions
STA: CA A2 15.0
TOP: 7-1 Example 1
KEY: real roots | square root
6. ANS: A
PTS: 1
DIF: L2
REF: 7-2 Multiplying and Dividing Radical Expressions
OBJ: 7-2.1 Multiplying Radical Expressions
TOP: 7-2 Example 3
KEY: multiplying radical expressions | simplifying a radical expression
7. ANS: A
PTS: 1
DIF: L2
REF: 7-4 Rational Exponents
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0
TOP: 7-4 Example 2
KEY: rational exponent | radical form
8. ANS: C
PTS: 1
DIF: L4
REF: 7-4 Rational Exponents
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0
TOP: 7-4 Example 2
KEY: rational exponent | radical form
9. ANS: A
PTS: 1
DIF: L2
REF: 7-4 Rational Exponents
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0
TOP: 7-4 Example 5
KEY: rational exponent
10. ANS: D
PTS: 1
DIF: L2
REF: 7-5 Solving Radical Equations
OBJ: 7-5.1 Solving Radical Equations
STA: CA A2 8.0
TOP: 7-5 Example 2
KEY: radical equation | rational exponent
11. ANS: B
PTS: 1
DIF: L2
REF: 7-5 Solving Radical Equations
OBJ: 7-5.1 Solving Radical Equations
STA: CA A2 8.0
TOP: 7-5 Example 4
KEY: radical equation | extraneous solutions
12. ANS: A
PTS: 1
DIF: L2
REF: 7-6 Function Operations
OBJ: 7-6.1 Operations with Functions
STA: CA A2 24.0 | CA A2 25.0
TOP: 7-6 Example 1
KEY: addition and subtraction of functions | operations with functions
13. ANS: B
PTS: 1
DIF: L2
REF: 7-6 Function Operations
OBJ: 7-6.1 Operations with Functions
STA: CA A2 24.0 | CA A2 25.0
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7-6 Example 1
addition and subtraction of functions | operations with functions
C
PTS: 1
DIF: L3
REF: 7-6 Function Operations
7-6.1 Operations with Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 2
addition and subtraction of functions | operations with functions
C
PTS: 1
DIF: L2
REF: 7-6 Function Operations
7-6.1 Operations with Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 2
operations with functions | multiplication and division of functions | domain
B
PTS: 1
DIF: L2
REF: 7-6 Function Operations
7-6.1 Operations with Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 2
multiplication and division of functions | operations with functions | domain
D
PTS: 1
DIF: L3
REF: 7-6 Function Operations
7-6.1 Operations with Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 2
multiplication and division of functions | operations with functions | domain
B
PTS: 1
DIF: L2
REF: 7-6 Function Operations
7-6.2 Composition of Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 3
KEY: composition of functions | operations with functions
D
PTS: 1
DIF: L3
REF: 7-6 Function Operations
7-6.2 Composition of Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 3
KEY: composition of functions | operations with functions
A
PTS: 1
DIF: L3
REF: 7-6 Function Operations
7-6.2 Composition of Functions
STA: CA A2 24.0 | CA A2 25.0
7-6 Example 3
KEY: composition of functions | operations with functions
C
PTS: 1
DIF: L2
REF: 7-7 Inverse Relations and Functions
7-7.1 The Inverse of a Function
STA: CA A2 24.0 | CA A2 25.0
7-7 Example 1
KEY: inverse relations and functions | relation | graphing
A
PTS: 1
DIF: L2
REF: 7-7 Inverse Relations and Functions
7-7.1 The Inverse of a Function
STA: CA A2 24.0 | CA A2 25.0
7-7 Example 2
KEY: inverse relations and functions |
B
PTS: 1
DIF: L2
REF: 7-7 Inverse Relations and Functions
7-7.1 The Inverse of a Function
STA: CA A2 24.0 | CA A2 25.0
7-7 Example 3
KEY: graphing | inverse relations and functions
B
PTS: 1
DIF: L2
REF: 7-7 Inverse Relations and Functions
7-7.1 The Inverse of a Function
STA: CA A2 24.0 | CA A2 25.0
7-7 Example 4
KEY: domain | inverse relations and functions | range
B
PTS: 1
DIF: L2
REF: 7-7 Inverse Relations and Functions
7-7.1 The Inverse of a Function
STA: CA A2 24.0 | CA A2 25.0
7-7 Example 6
KEY: composition of functions | inverse relations and functions
A
PTS: 1
DIF: L2
REF: 7-8 Graphing Radical Functions
7-8.1 Radical Functions
TOP: 7-8 Example 1
domain | graphing | range | radical function | translation
C
PTS: 1
DIF: L2
REF: 7-8 Graphing Radical Functions
7-8.1 Radical Functions
TOP: 7-8 Example 2
domain | graphing | range | radical function | translation
C
PTS: 1
DIF: L2
REF: 7-8 Graphing Radical Functions
OBJ:
KEY:
29. ANS:
OBJ:
KEY:
30. ANS:
OBJ:
KEY:
7-8.1 Radical Functions
TOP: 7-8 Example 3
domain | graphing | range | radical function
C
PTS: 1
DIF: L2
REF: 7-8 Graphing Radical Functions
7-8.1 Radical Functions
TOP: 7-8 Example 3
domain | graphing | range | radical function | translation
B
PTS: 1
DIF: L2
REF: 7-8 Graphing Radical Functions
7-8.1 Radical Functions
TOP: 7-8 Example 3
domain | graphing | range | radical function | translation