Activity 3.2 Changes in Input and Output
Overview:
A table of values of miles driven and the number of gallons of gas used is given and students are
asked to explain what different function notation values represents.
Estimated Time Required:
This activity should take approximately 20 minutes.
Technology: None
Concepts:
Evaluating a function using function notation
The effects of addition to input and output
Discussion:
A major goal of the course is to move students towards a more global view of functions as objects
that model particular situations. You may want to discuss the interpretive aspects of function
notation and language, as shown in Example 2 and 3 in the text, before given students the
activity.
Activity 3.2 Changes in Input and Output
Problem 1
A car averages 20 miles per gallon of gas. Complete the table below.
m = number of miles driven
n = number of gallons of gasoline used
m
n = f(m)
f(m+30)
f(m) + 30
0
0
1.5
30
Explain what f(m + 30) means.
Explain what f(m) + 30 means.
20
1
2.5
31
40
2
3.5
32
60
3
4.5
33
80
4
5.5
34
100
5
6.5
35
Problem 2
Now consider g, as a function of the number of gallons.
n
m = g(n)
g(n+30)
g(n) +30
1
20
620
50
Explain what g(n + 30) means.
Explain what g(n) + 30 means.
2
40
640
70
3
60
660
90
4
80
680
110
5
100
700
130
6
120
820
150
0
