Lesson 7
Connecting Representations of Functions
Let’s connect tables, equations, graphs, and stories of functions.
Problem 1
The equation and the tables represent two different functions. Use the equation \(b=4a5\) and the table to answer the questions. This table represents \(c\) as a function of \(a\).
\(a\)  3  0  2  5  10  12 

\(c\)  20  7  3  21  19  45 
 When \(a\) is 3, is \(b\) or \(c\) greater?
 When \(c\) is 21, what is the value of \(a\)? What is the value of \(b\) that goes with this value of \(a\)?
 When \(a\) is 6, is \(b\) or \(c\) greater?
 For what values of \(a\) do we know that \(c\) is greater than \(b\)?
Problem 2
Elena and Lin are training for a race. Elena runs her mile at a constant speed of 7.5 miles per hour.
Lin’s total distances are recorded every minute:
time (minutes)  1  2  3  4  5  6  7  8  9 

distance (miles)  0.11  0.21  0.32  0.41  0.53  0.62  0.73  0.85  1 

Who finished their mile first?

This is a graph of Lin’s progress. Draw a graph to represent Elena’s mile on the same axes.

For these models, is distance a function of time? Is time a function of distance? Explain how you know.
Problem 3
Match each function rule with the value that could not be a possible input for that function.
Problem 4
Find a value of \(x\) that makes the equation true. Explain your reasoning, and check that your answer is correct.
\(\displaystyle \text(\text2x+1)= 914x\)