1. Chapter 3: Functions and Graphs 3.6: Inverse Functions Essential Question: How do we algebraically determine the inverse of a function

2. 3-6: Inverse Functions To invert a function, switch x and y values. ▫That is, if a point (a, b) is on the graph of f, then the point (b, a) is on the graph of the inverse. Example: Write a table that represents the inverse of the function given by the table. ▫ xf(x) 4 03 14 21 35 yf(y) 4 30 41 12 53

3. 3-6: Inverse Functions To invert a function algebraically, swap x and y values, then try to solve the equation for y. Example ▫y = 3x – 2

4. 3-6: Inverse Functions Example ▫f(x) = x 2 + 4x ▫y = x 2 + 4x

5. 3-6: Inverse Functions You can determine if a graph is a function by using the vertical line test A graph is considered one-to-one, if it’s inverse is also a function You can determine a graph is one-to-one by using a horizontal line test

6. 3-6: Inverse Functions Determine if the following graphs are one-to-one ▫ f(x) = 7x 5 + 3x 4 – 2x 3 + 2x + 1 ▫ ▫ g(x) = x 3 – 3x – 1 ▫ Yes, the graph is one-to-one No, the graph is not one-to-one

7. 3-6: Inverse Functions Assignment ▫Page 212 – 213 ▫Problems: 1, 9 – 19 (odd), 23 – 29 (odd)