# 2.1: Back in Time?

*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 , Marty is at position .

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 of what it is on Earth. So with , use the distance formula to compute the output when given the input.

5. Use the formula to compute . Give the set or ordered pairs when the input is the set .

6. Use the formula to compute . Give the set of ordered pairs if the input is . The input set for is .

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. is a function of

B. is a function of

C. both

D. neither

## Problem 3 – Function Notation

If is a function of this can be written as .

For example, . So .

To use the function ability of your graphing calculator, press and enter .

Return to the Home screen.

To enter different values for and observe what equals, press **VARS**, arrow right to the **Y-VARS** menu, select **Function** and then choose . Then enter **(#)**, replacing # with the value.

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

9. For , find using the graphing calculator, then by substitution showing your work below.

10. For , find using the graphing calculator, then by substitution showing your work below.

## 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 that gives an output of ?

12. What is the unknown function?

Now select option **2**.

13. What is the input for the function that gives an output of ?

14. What is the unknown function?

Now select option **3**.

15. What is the input for the function that gives an output of ?

16. What is the unknown function?