4 7 Inverse Linear Functions ALGEBRA 1 Content

4. 7 Inverse Linear Functions ALGEBRA 1

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. 4 a 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.

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) = – 3 x + 27. 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) = 2200 + 0. 05 x. A. Find the inverse function.

Example 5 B 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. 05 x. B. What do x and f – 1(x)represent in the context of the inverse function?

Example 5 C 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. 05 x. C. Find Carter’s total sales for last month if his earnings for that month were $3450.

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