Compare Two Functions by Analyzing an Equation and a Graph

This lesson teaches how to compare two functions by analyzing equations and graphs. It explains that a graph is a visual representation of a function, while an equation is an algebraic representation. The lesson uses real-world examples, such as recycling programs in California and Michigan, to illustrate these concepts. It emphasizes understanding the rate of change and y-intercept in equations and graphs, and highlights the importance of recognizing one-to-one functions. The lesson concludes by summarizing the key points about comparing functions.

What is the primary purpose of a graph in relation to a function?

• To calculate the function's output

• To provide an algebraic representation

• To show a visual representation

• To determine the function's input

In an equation, what does the coefficient of x represent?

• The rate of change

• The input value

• The constant

• The y-intercept

What is the equation for the recycling program in California?

• y = 0.05x

• y = x + 5

• y = 2x

• y = 0.10x

How much does Michigan offer for recycling one soda can?

• $0.20

• $0.05

• $0.10

• $0.15

What defines a one-to-one function?

• Each output has a unique input

• Multiple inputs for a single output

• A single input for multiple outputs

• Each input has a unique output

Which state has a greater rate of change in their recycling program?

• Neither has a rate of change

• Both have the same rate

• Michigan

• California

What is the y-intercept in a function's graph?

• The input value

• The rate of change

• The coefficient of x

• The value of y when x is 0