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 relationship between a graph and a function?

What is an input-output pair and how is it represented on a graph?

How can you determine if a relation is a function from an equation?

Describe how to identify a one-to-one function from a graph.

Compare the rate of change for California and Michigan's recycling programs.

Explain the significance of the rate of change in a function.

What does the y-intercept represent in a function?