Honors Precalculus October 25, 2016 Mrs. Agnew Inverse Functions Honors Precalculus October 25, 2016 Mrs. Agnew

Essential Question Essential Vocabulary How do you find the inverse of a function? How do you evaluate a function composition? Essential Vocabulary One-to-one function Inverse Function Function Composition

One-to-One Functions What is a one-to-one function? A relation in which every x value is matched to exactly one y value (function) and every y value is matched to exactly one x value (one-to-one). How do we determine if a function is one-to-one?

Inverse Relations To have an inverse, a function must be one-to-one. The inverse of a function switches all the x and y values. The graph of an inverse is a reflection over the line y = x.

Finding Inverses To find the inverse of a given function: Switch the x and y Solve for y Label inverse with f -1(x) Page 269 #44 – 48, 52, 56, 60, 66, 70, 74

To Make You Think… 1. Is the inverse of a function a function? 2. Do all functions have inverses? 3. Do all linear functions have inverses? 4. What is the slope of the inverse of a linear function?

Homework: 10/25/16 Page 269 – 270 #43, 45, 51, 55, 63, 67, 73, 75, 77, 81