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.

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.

  1. Speed is a function of time.
  2. Time is a function of distance.
  3. Speed is a function of number of students racing.
  4. 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.

 

(From Unit 4, Lesson 15.)

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