Lesson 7: 4-7 Inverse of Linear Functions

What ordered pair is the inverse of (a, b)?

How can you graph the inverse of a relation or function?

What do you notice about the slopes of lines and their inverses?

• How do you find the inverse of a linear function?

inverse relation
inverse function

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.

SAT questions related to writing equations: 5-4-11,4-3-8,8-4-7,1-3-12,7-3-19
functions: 8-4-4, 7-4-18, 8-4-18, 2-4-14, 3-4-20, 1-4-5, 7-4-21,
Solving Equations: 5-3-17, 6-4-32, 3-4-7, 8-3-1, 3-3-17, 6-3-17, 1-3-1, 3-3-2, 2-3-1, 7-3-16, 6-3-6,

An inverse relation is the set of ordered pairs obtained by exchanging the x-coordinate with the y-coordinate of each ordered pair of a relation. A linear function f(x) has an inverse function f–1(x) that can be found by replacing f(x) with y, interchanging x and y in the equation, solving for y, and then replacing y with f(x).

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.
b. What do x and f-1(x) represent in the context of the inverse function?
c. Find Carter's total sales for last month if his earnings for that month were $3450.

Interpersonal Learners: Write the equation of a linear function on an index card. Sketch the graph of the function on a second card. On a third card, display a table of points for the function. Repeat this process for the inverse of the function. Create similar cards for several functions and their inverses. Have students work in groups of two or three. Give each group a copy of all of the cards. Have the groups divide the cards by matching each equation with its graph and table, and then with the equation, graph, and table of its inverse.

Extension: Have students graph the inverse of y = x2. First, have students graph y = x2 on a coordinate plane by creating a table of points. Then, have them find points on the graph of the inverse by exchanging the x-coordinates with the y-coordinates of each ordered pair in the table. Have students plot these new points on the same coordinate plane. Finally, have students connect the new points with a smooth curve, using the graph of y = x2 as a guide. Remind students that the graphs of inverse relations are reflections of each other in the line y = x.

Practice: Exercises 1-7

Exercises 44- 52

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