Connecting Function Notation to Graphs
1. Given the graph f(x), answer the following. Unless otherwise specified, restrict the domain of the function to
the interval [-6, 7]. Approximations are appropriate answers.
a. What is f(2)?
b. For what values, if any, does ( )
?
c. Give one root of f(x).
d. What is the solution set of ( )
?
e. What is ( ( ))?
f.
On what intervals is ( )
?
g. On what intervals is f(x) increasing?
h. On what intervals is the rate of increase of f(x) decreasing?
i.
For what values, if any, does ( )
j.
What do you think is a reasonable way to continue the graph past x = 7? On the basis of your
continuation, what is ( )?
?
2. Consider the graphs of f(t) and g(t). Restrict the
domain to the interval [-5, 7].
a. Where is ( )
( )?
b. Where is ( )
( )?
c. Where is ( )
( )
?
d. On the interval [1, 4], where is
( )
( ) increasing?
e. What Is ( ( ))?
b. Over what time intervals is the total output produced
by the generators greater than 30 volts?
c. Over what intervals is the voltage from generator A
decreasing at a faster rate than that from generator B?
Output (volts)
3. Consider the graph
a. Over what time intervals is the voltage from
generator A greater than that from generator B?
d. At what time(s) is the output from the two generators
exactly double the output from generator A?
Time (min)
4. Given the table, answer the following questions:
x
f(x)
-5
42
-4
30
-3
20
-2
12
-1
6
0
2
1
0
2
0
3
2
4
6
5
12
6
20
g(x)
-13
-9
-5
-1
3
7
11
15
19
23
27
31
a. What is g(-3)?
b. For what value(s) is ( )
?
c. For what values is f(x) increasing?
d. On what interval is ( )
( )?
e. Which function is changing faster in the interval [-5, 0]? Why?
What is ( (
))?
g. What is ( (
))?
f.
5. Given f(x) and g(x):
f(x)
g(x)
Find the graph of the following:
( )
( )
[A]
( )
[B]
( )
( )
( )
[C]
Connecting Context to Notation
Given graph A, B, or C, define a possible practical context for f(x) and g(x) such that the resulting operation on those
functions would have meaning. Identify the meaning of the resulting function.
Use the context you created to determine the meaning for the other two operations on function f(x) and g(x), if
appropriate:
[A] ( )
[B] ( )
[C]
( )
( )
( )
( )