Name ___________________________________
Date __________
Period ___
Quiz – Comprehensive
1. Describe the end behavior of the function k x   2 log 5 x  3  6 .
A
As x  3, f ( x)   and as x  , f ( x)   .
B
As x  , f ( x)  3 and as x  , f ( x)   .
C
As x  3, f ( x)   and as x  , f ( x)  0 .
D
As x  , f ( x)  3 and as x  , f ( x)  0 .
2. Which equation represents the graph below?
A


2
( x  2)  3, x  2
5
f ( x)   x  3,  2  x  0
2
  1 x
   , x  0
 2
C

( x  2) 2  3, x  2

5
f ( x)   x  3,  2  x  0
2
 1
 x , x  0
B
D

( x  2) 2  3, x  2

5
f ( x)   x  3,  2  x  0
2
 1
 x , x  0

( x  2) 2  3, x  2

5
f ( x)   x  3,  2  x  0
2
 1
 x , x  0
3. The end behavior of a function, w ( x ) , can be described as x   , w( x )   . Which function could represent
w( x ) ?
A
w( x )  (4  x )( 2  x )( x  3) 2
C
w( x )  ( x  2) 2 (3  x )( x  4)
w( x )  ( x  1)( 2  x ) 2 ( x  3)
D w ( x )  (5  x )( 4  x )( 3  x )
B
4. Which of the following statements describes a feature of the graph of f ( x)  
14 3
x ?
2
I The graph is decreasing on the interval (0, ∞).
II The range is [0, ∞).
III The domain is [0, ∞).
A I and III only
B I and II only
C II and III only
D I, II and III
5. The equations for rational functions f ( x ) and g ( x ) are given below.
f ( x) 
3x 2  3
x2  9
g ( x) 
x2
x3  9 x
Which statement below is correct about the two functions?
A Both functions are odd functions.
B f is an even function and g is an odd function.
C Both functions are even functions.
D f is an odd function and g is an even function.
6. Which statement(s) is true about the graph of f ( x) 
I
II
III
The graph of f has a discontinuity at x  3
The behavior of f around x  3 is the same from both the positive and negative directions.
The behavior of f is the same as x goes to positive infinity and negative infinity.
A I and II only
B II and III only
7. What is the solution to the inequality
A
x 2  x  12
?
( x  3)2
 13 
 ,4
6 
B
C I and III only
2x  4
 12 ?
( x  3)2
 13 
 ,3    3, 4 
6 
C
(, 2)  (3, )
8. Which equations would represent graphs with equivalent domain and ranges?
I
II
III
A
B
C
D
2
4
x3
4 x 2  6 x  10
h( x )  2
x  2x  3
4 x  10
v( x) 
x 3
g ( x) 
I and III only
I and II only
II and III only
I, II and III
D I, II and III
D
13 

 ,    4,  
6

9. Which function listed below is the inverse of f ( x)  4 x 1  6 ?
A
f 1 ( x)  log 4 x  6  1
C
f 1 ( x)  log 4 x  6  1
B
f 1 ( x)  log 4 x  6  1
D
f 1 ( x)  log 4 x  6  1
10. Given the functions:
g ( x)  2 x  4
f ( x)  x 2
h( x )  x  3
Which of the following functions can be written as composition of the functions above?
I
II
III
w( x)  (2 x  4) 2  3
k ( x)  2( x 2  3)  4
t ( x)  2 x 2  3  4

A I and II only
C II and III only

B I and III only
D I, II, and III only
11. Given the function f ( x) 
1 x 3
 4  5 , which of the following is not true about the graph of f?
2
A
The graph of f is increasing across its entire domain.
B
The graph of f does not have an x-intercept.
C
The graph of f has a vertical asymptote at x=5.
D
The graph of f has a range of 5,   .
12. Which graph correctly describes the end behavior of the graph of f ( x) 
A As x   , f ( x )  2
C As x   , f ( x)  2
(2 x  1)(3  2 x)
?
(2 x  1)( x  3)
B As x   , f ( x)  1
D As x   , f ( x)  1
13. Logan solved the following equation, and determined that there was no solution. Maddi thinks he made a mistake.
If Logan’s solution is incorrect, in which step did he make his first error?
ln x  5  ln x  1  ln x  1
Step 1
ln x  5  ln x  1  x  1
Step 2
ln x  5  ln  2
x  5  2
x  7 , therefore there is no
solution
Step 3
Step 4
A
Step 1
B
Step 2
C
Step 3
D
No mistakes made
14. The graph below represents the dosage for a children’s pain reliever.
Dosage (ml)
Dosage Guidelines
Child’s Weight (lbs.)
Which statement can be concluded from the graph?
A
B
C
D
A child weighing 30 pounds receives half the dosage of a child weighing 50 pounds.
A child weighing 90 pounds receives twice the dosage of a child weighing 48 pounds.
A child weighing 35 pounds receives the same dosage as a child weighing 36 pounds.
A child weighing 70 pounds receives three times the dosage of a child weighing 35 pounds.
15. The table below contains coordinates from the graph of f.
x
2
3
5
9
17
y
3
3.5
4
4.5
5
Which function represents f
A
g ( x)  2.5
B
g ( x)  0.128  2.5
x2
 .5
x
1
?
C
g ( x)  4 x 1  3
D
g ( x )  4 x 3  1