ALGEBRA 1 4.7 Inverse Linear Functions. Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities;

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ALGEBRA Inverse Linear Functions

Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F.BF.4a Solve an equation of the form f (x ) = c for a simple function f that has an inverse and write an expression for the inverse. Mathematical Practices 6 Attend to precision. Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

You represented relations as tables, graphs, and mappings. Find the inverse of a relation. Find the inverse of a linear function.

Inverse Relations

Example 1 A. Find the inverse of each relation. {(−3, 26), (2, 11), (6, −1), (−1, 20)}

You Try! B. Find the inverse of each relation.

Example 2 A. Graph the inverse of each relation. Find some points that cross nicely on the graph! Flip the x and y values of those points, then graph!

You Try! B. Graph the inverse of each relation.

Finding Inverse Equations Follow these steps… 1) Replace f(x) with y! 2) Flip x and y 3) Solve for y 4) Change y back to f -1 (x)

Example 3 A. Find the inverse of the function f (x) = –3x Step 1: Step 2: Step 3: Step 4:

Example 4 You Try!

Example 5 SALES Carter sells paper supplies and makes a base salary of $2200 each month. He also earns 5% commission on his total sales. His total earnings f(x) for a month in which he compiled x dollars in total sales is f(x) = x. A. Find the inverse function.

Example 5B SALES Carter sells paper supplies and makes a base salary of $2200 each month. He also earns 5% commission on his total sales. His total earnings f(x) for a month in which he compiled x dollars in total sales is f(x) = x. B. What do x and f –1 (x)represent in the context of the inverse function?

Example 5C SALES Carter sells paper supplies and makes a base salary of $2200 each month. He also earns 5% commission on his total sales. His total earnings f(x) for a month in which he compiled x dollars in total sales is f(x) = x. C. Find Carter’s total sales for last month if his earnings for that month were $3450.

End of the Lesson  Mini Practice Activity  Homework: On the back of your notes sheet!