1. ALGEBRA 1 4.7 Inverse Linear Functions

2. 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 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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

4. Inverse Relations

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

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

7. 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!

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

9. 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)

10. Example 3 A. Find the inverse of the function f (x) = –3x + 27. Step 1: Step 2: Step 3: Step 4:

11. Example 4 You Try!

12. 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) = 2200 + 0.05x. A. Find the inverse function.

13. 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) = 2200 + 0.05x. B. What do x and f –1 (x)represent in the context of the inverse function?

14. 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) = 2200 + 0.05x. C. Find Carter’s total sales for last month if his earnings for that month were $3450.

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