1. 7.7 Inverse Relations and Functions

2. Using a graphing calculator, graph the pairs of equations on the same graph. Sketch your results. Be sure to use the negative sign, not the subtraction key. What do you notice about the graphs? These graphs are said to be inverses of each other.

3. An inverse relation “undoes” the relation and switches the x and y coordinates.  In other words, if the relation has coordinates (a, b), the inverse has coordinates of (b,a) XY 03 14 -30 -52 25 -85XY30 41 0-3 2-5 52 5-8 Function f(x)Inverse of Function f(x)

4. Let’s look at our graphs from earlier. Notice that the points of the graphs are reflected across a specific line. What is the equation of the line of reflection? y = x

5. Finding the Inverse of an equation Find the inverse of y=x 2 +3 x=y 2 +3 x – 3 = y 2 Switch the x and y Solve for y Find the square root of both sides

6. What happens if I don’t include the + ?  Graphing the function and only the positive graph of the inverse... We only get half of the inverse graph.

7. Finding the Inverse of a function Rewrite using y Switch the x and y Square both sides Solve for y When we find the inverse of a function f(x) we write it as f -1 Find the inverse of

8. Let’s Try Some Find the inverse of each

9. Let’s Try Some Find the inverse of each

10. Composition of Inverse Functions For the function