Avon High School
College Algebra
Name ____________________________
Period _____
Score ______ / 10
Worksheet 2.4A
In 1-8, match the graph to its function.
A. Constant Function
D. Cube Function
G. Absolute Value Function
B. Identity Function
E. Square Root Function
H. Cube Root Function
C. Square Function
F. Reciprocal Function
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
In 9-12, sketch the graph of each function. Be sure to label three points on the graph.
9.) f  x   x
10.) f  x   x3
REVIEW
Use the graph of the function f to answer 1-2.
1.) Is f decreasing on the interval  8,  4 ?
2.) List the interval(s) on which f is decreasing.
11.) f  x  
1
x
12.) f  x  
3
x
Use the graph of the function f to answer 3-6.
3.) Find the x- and y-intercepts, if any.
4.) State the domain and range.
5.) State the intervals on which it is
increasing, decreasing, or constant.
Use the graph of the function f to answer 7-8.
7.) Find the values, if any, at which f has a
local maximum.
What are these local maxima?
6.) Is the function even, odd, or neither?
8.) Find the values, if any, at which f has a
local minimum.
What are these local minima?
Determine algebraically whether each function is even, odd, or neither.
9.) f  x   2 x4  x2
10.) f  x   3 2 x2  1
Determine whether the relation represents a function. If so, state the domain and range.
11.)
 2, 4 ,  1,1 ,  0,0 , 1,1
Determine whether the equation defines y as a function of x.
12.) y  2 x 2  3x  4
Find the domain of each function.
x2
13.) f  x   2
x 1
14.) h  x  
2x
x 4
2
For the given functions f and g, find the following. For parts (a)-(d), also find the domain.
15.) f  x   1 
1
1
; g  x 
x
x
a.)
 f  g  x 
b.)
 f  g  x 
c.)
 f  g  x 
e.)
 f  g 3
f.)
 f  g  4
g.)
 f  g  2
Use the graph of the function f to answers parts (a)-(p).
1.)
a.) Find f  0  . b.) Find f  6  .
c.) Find f  2  .
e) Is f  3 positive or negative?
f.) Is f  1 positive or negative?
g.) For what values of x is
f  x  0 ?
h.) For what values of x is
f  x  0 ?
i.) What is the domain of f?
j.) What is the range of f?
k.) What are the x-intercepts?
l.) What are the y-intercepts?
m.) How often does the line
y  1 intersect the graph?
n.) How often does the line x  1
intersect the graph?
o.) For what values of x does
f  x  3 ?
p.) For what values of x does
f  x   2 ?
d.) Find f  2  .
f 
  x
g
d.) 
f 
 1
g
h.) 
Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:
a.) The domain and range
b.) The intercepts, if any
c.) Any symmetry with respect to the x-axis, the y-axis, or the origin
2.)
3.)
4.)
Answer the questions about the given function.
5.) f  x   3x 2  5x
a.) Is the point  1, 2  on the graph of f?
b.) If x  2 ,what is f  x  ?
What is the point on the graph of f?
c.) If f  x   2 , what is x?
d.) What is the domain of f?
What point(s) are on the graph of f?
e.) List the x-intercepts, if any, of the graph of f.
f.) List the y-intercept, if there is one, of the graph of f.
The graph of an equation is given. Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or
the origin.
9.)
List the intercepts and test for symmetry.
10.) y 
x2  4
2x