How do you make comparisons between an equation

How do you make comparisons between an equation and a table? y = -2 x + 1 Input Output 1 -1 2 -3 3 -5 4 -7 5 -9 6 -11

In this lesson you will learn how to compare two functions by analyzing an equation and a table.

Let’s Review A table is a numeric representation of the inputs and outputs of a function relation. Input Output 1 2 3 2 4 6 Input Output 1 2 2 4 3 6 4 8 5 10 6 12

Let’s Review An equation is an algebraic representation of a function relation. Input Output 1 2 3 2 4 6 or Output = 2 * Input y = 2 x

A Common Let’s Review Mistake Input Output -1 -2 0 0 5 10 7 14 9 18 15 30 Constant 18 – 14 = rate 4 14 – 10 4 18 – 14 =rate 4 =of 2 Constant of 14 change =10 ===4 42 – 7– – 7 5 2= 22 9 change No !!

Core. Review Lesson Let’s California offers $0. 05 for every soda can brought in to recycle. Input (x) Output (y) (cans) rate (money) constant of change y = 0. 05 x 0. 05 1 = 0. 05 = 2 3 0. 10 0. 15

Core. Review Lesson Let’s Michigan offers $0. 10 for every soda can brought in to recycle. Soda cans (x) Money (y) 13 4 25 10 3 0. 30 0. 10 0. 40 0. 20 0. 50 1. 00 0. 30 Input (x) Output (y) 1 0. 10 (cans) (money) 2 0. 20 =

Core. Review Lesson Let’s y = 0. 05 x • Function • One-to-one • Constant rate of change = 0. 05 Soda cans (x) Money (y) 1 0. 10 2 0. 20 3 0. 30 4 0. 40 5 0. 50 10 1. 00 • Function • One-to-one • Constant rate of change = 0. 10

Core. Review Lesson Let’s Input (x) Output (y) -2 14 3 4 6 -2 8 -6 10 -10 15 -20 -6 -2 -4 -6 – -2 4 rate of Constant == 682 –– 336 = -2 change

In this lesson you have learned how to compare two functions by analyzing an equation and a table.

Guided Practice Let’s Review Which function relation shows the smaller rate of change? A. B. Input (x) y = 5 x A) Neither 1 2 B) Function A 3 C) Function B 4 5 D) Both functions A and B Output (y) 6 12 18 24 30

Extension Let’s Review. Activities Verizon’s “Share everything” plan costs are shown at right for 1 smartphone and a monthly “GB allowed. ” Is this plan a linear relation? Explain using rates of change. GB allowed 1 Cost 2 100 4 110 6 120 8 130 10 140 90

Extension Let’s Review. Activities A grocery store has a special on apples and oranges. How much is each apple and each orange? Apples Cost Oranges Cost 5 10 15 $3. 00 $6. 00 $9. 00 4 8 12 $5. 00 $10. 00 $15. 00

Quick Quiz Let’s Reviewis the rate of change for the What given function representation? What would 3 marbles cost? Marbles Cost 1 4 6 0. 25 1. 00 1. 50 8 12 2. 00 3. 00