Lesson 7Connecting Representations of Functions
Learning Goal
Let’s connect tables, equations, graphs, and stories of functions.
Learning Targets
I can compare inputs and outputs of functions that are represented in different ways.
Lesson Terms
- dependent variable
- independent variable
- radius
- volume
Warm Up: Which are the Same? Which are Different?
Problem 1
Here are three different ways of representing functions. How are they alike? How are they different?
Activity 1: Comparing Temperatures
Problem 1
The graph shows the temperature between noon and midnight in City A on a certain day.
The table shows the temperature,
Which city was warmer at 4:00 p.m.?
Which city had a bigger change in temperature between 1:00 p.m. and 5:00 p.m.?
How much greater was the highest recorded temperature in City B than the highest recorded temperature in City A during this time?
Compare the outputs of the functions when the input is 3.
Activity 2: Comparing Volumes
Problem 1
The volume,
Here is an applet to use if you choose.
Is the volume of a cube with edge length
greater or less than the volume of a sphere with radius 3? Estimate the radius of a sphere that has the same volume as a cube with side length 5.
Compare the outputs of the two volume functions when the inputs are 2.
Print Version
The volume,
Is the volume of a cube with edge length
greater or less than the volume of a sphere with radius 3? If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere.
Compare the outputs of the two volume functions when the inputs are 2.
Are you ready for more?
Problem 1
Estimate the edge length of a cube that has the same volume as a sphere with radius 2.5.
Activity 3: It’s Not a Race
Problem 1
Elena’s family is driving on the freeway at 55 miles per hour.
Andre’s family is driving on the same freeway, but not at a constant speed. The table shows how far Andre’s family has traveled,
How many miles per minute is 55 miles per hour?
Who had traveled farther after 5 minutes? After 10 minutes?
How long did it take Elena’s family to travel as far as Andre’s family had traveled after 8 minutes?
For both families, the distance in miles is a function of time in minutes. Compare the outputs of these functions when the input is 3.
Lesson Summary
Functions are all about getting outputs from inputs. For each way of representing a function—equation, graph, table, or verbal description—we can determine the output for a given input.
Let’s say we have a function represented by the equation
If we had a graph of this function instead, then the coordinates of points on the graph are the input-output pairs. So we would read the
A table representing this function shows the input-output pairs directly (although only for select inputs).
Again, the table shows that if the input is 2, the output is 8.