# 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 $$b=4a-5$$ and the table to answer the questions. This table represents $$c$$ as a function of $$a$$

 $$a$$ $$c$$ -3 0 2 5 10 12 -20 7 3 21 19 45
1. When $$a$$ is -3, is $$b$$ or $$c$$ greater?
2. When $$c$$ is 21, what is the value of $$a$$? What is the value of $$b$$ that goes with this value of $$a$$?
3. When $$a$$ is 6, is $$b$$ or $$c$$ greater?
4. 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) distance (miles) 1 2 3 4 5 6 7 8 9 0.11 0.21 0.32 0.41 0.53 0.62 0.73 0.85 1
1. Who finished their mile first?

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

3. 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.

(From Unit 5, Lesson 2.)

### Problem 4

Find a value of $$x$$ that makes the equation true. Explain your reasoning, and check that your answer is correct.

$$\displaystyle \text-(\text-2x+1)= 9-14x$$

(From Unit 4, Lesson 4.)