Lesson 2
Introduction to Functions
Let’s learn what a function is.
Problem 1
Here are several function rules. Calculate the output for each rule when you use -6 as the input.
![Six function rule diagrams, no input or output given for any.](https://staging-cms-im.s3.amazonaws.com/SMw4mYzy6LJP4YW8U682zTg9?response-content-disposition=inline%3B%20filename%3D%228-8.5.New.Image.PP.86.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.New.Image.PP.86.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150708Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=632d170ea355c8aba95bc3a92075017febc1dd98bc7d9e849e6b784e53cfe29d)
Problem 2
A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is each statement true or false? Explain your reasoning.
- Speed is a function of time.
- Time is a function of distance.
- Speed is a function of number of students racing.
- Time is a function of speed.
Problem 3
Diego’s history teacher writes a test for the class with 26 questions. The test is worth 123 points and has two types of questions: multiple choice worth 3 points each, and essays worth 8 points each. How many essay questions are on the test? Explain or show your reasoning.
Problem 4
These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not? Explain or show your reasoning.
Table A:
input | output |
---|---|
-2 | 4 |
-1 | 1 |
0 | 0 |
1 | 1 |
2 | 4 |
Table B:
input | output |
---|---|
4 | -2 |
1 | -1 |
0 | 0 |
1 | 1 |
4 | 2 |
Table C:
input | output |
---|---|
1 | 0 |
2 | 0 |
3 | 0 |
Table D:
input | output |
---|---|
0 | 1 |
0 | 2 |
0 | 3 |