# 2.1: Back in Time?

**At Grade**Created by: CK-12

*This activity is intended to supplement Algebra I, Chapter 1, Lesson 5.*

## Definition

A *function* is a relation in which each input is paired with exactly **one** output.

For every value that goes into a function, the function outputs one unique result.

## Problem 1 – Graphical

At time

1. Can the graph to the right describe Marty’s position as a function of time? Explain.

2. What would have to happen for this graph to occur?

3. Redraw the dashed lines to make the graph a function.

## Problem 2 – Set of Ordered Pairs

The first element of each ordered pair is the input value.

4. Which sets below describe a function? Explain why.

A.

B.

C.

D.

Marty flies to Mars, where the acceleration of gravity is

5. Use the formula to compute

6. Use the formula to compute

7. Which of the two solutions sets from Questions 5 and 6 is a function? Why?

8. From solutions sets above, which is true?

A.

B.

C. both

D. neither

## Problem 3 – Function Notation

If

For example,

To use the function ability of your graphing calculator, press

Return to the Home screen.

To enter different values for **VARS**, arrow right to the **Y-VARS** menu, select **Function** and then choose **(#)**, replacing # with the

Press **[ENTER]** to recall the last entry.

9. For

10. For

## Problem 4 – Function Machine

Run the program **MACHINE** and select option **1**. The program will return an output for the input entered.

11. What is the input for the function

12. What is the unknown function?

Now select option **2**.

13. What is the input for the function

14. What is the unknown function?

Now select option **3**.

15. What is the input for the function

16. What is the unknown function?

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