1. Date: 0.7 Notes: Inverse Linear Functions Lesson Objective: Find the inverse of a relation. Find the inverse of a linear function. CCSS: A.CED.2 Create equations in 2 or more variables to represent relationships between quantities; graph equations. F.BF.4a Solve an equation and find its inverse. What does inverse mean?

2. From Merriam-Webster: INVERSE 1: opposite in order, nature, or effect Inverse Relation: The set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair in a relation.

3. Lesson 1: Inverse Relations Look at the graph of y = 3x and its inverse from the 0.7 Algebra Lab. List 4 points of y = 3x and 4 points of the inverse of y = 3x. y = 3xInverse of y = 3x What do you notice about the points? xy xy

4. Lesson 2: Finding the inverse relation with Mrs. Dawson. Find the inverse of the relation. {(5, -7), (-7, -11), (-3, 8), (0, 6)}

5. Lesson 3: Graphing Inverse Relations Graph the relation, then graph the inverse of the relation.

6. Lesson 4: Finding Inverse Linear Functions with Mrs. Workman Find the inverse of f(x) = 9 + 6x.

7. Lesson 5: A Real Life App with Mr. Rutherford The total cost C(x) in dollars is given by C(x) = 80 + 75x, where x is the # of hours it takes the contractor to complete the repairs. a.Find the inverse function C -1 (x). b.What do x and C -1 (x) represent in the context of the inverse function? c.Find the number of hours spent for repairs that cost $267.50.

8. 0.7: Do I Get It? (DIGI) Yes or No 1.Find the inverse of the relation {(4, -10), (7, -19), (-5, 17), (-3, 11)}. 2.Graph the relation, then graph the inverse of the relation. 3.Find the inverse of f(x) = 4x – 8.

9. 0.7: DIGI (cont.) EXTRA CREDIT! 4.Randall wants to convert the temperature from degrees Celsius to degrees Fahrenheit. The function to convert to Celsius is C(x) = 5 / 9 (x – 32). a.Find the inverse function C -1 (x). b.What do x and C -1 (x) represent in the context of the inverse function? c.Find the average temperatures for July in degrees Fahrenheit if the minimum and maximum averages are 3°C and 15°C, respectively.

10. Answers: 1.{(-10, 4), (-19, 7), (17, -5), (11, -3)} 2. 3.f⁻¹(x) = x + 8 4 or f⁻¹(x) = ¼x + 2

11. Answers: 4a.C -1 (x) = 9/5x + 32 b.X represents the temperature in degrees Celsius. C -1 (x) represents the temperature in degrees Fahrenheit. c.C -1 (3) = 37.4, C -1 (15) = 59