1. Warm-Up
For the following, make a T-Chart and sketch a graph for x ={-2, -1, 0, 1, 2}

2. Finding Inverses by Graphing

3. Things to know… The inverse of a function is denoted by
To graph an inverse: Make a table, switch x and y, re-graph
The inverse is the graph reflected over the line y=x.
THIS MEANS THAT THE DOMAIN of f(x) becomes the range of the inverse and the RANGE of f(x) becomes the domain of the inverse.

4. THIS INVERSE IS NOT A FUNCTION
THIS INVERSE IS NOT A FUNCTION! How can we look at the original to determine if its inverse will be a function? x y 4 -2 1 -1 2 x y -2 4 -1 1 2

5. x y 1 2 4 3 9 16 x y 1 4 2 9 3 16

8. INVERSE
FUNCTIONS

9. Remember we talked about functions---taking a set X and mapping into a Set Y1 2 3 4 5 10 8 6 1 2 2 4 3 6 4 8 10 5
Set X
Set Y
An inverse function would reverse that process and map from SetY back into Set X

10. If we map what we get out of the function back, we won’t always have a function going back!!!1 2 2 4 3 6 4 8 5
A relation is called a function when each input (x) maps to only one output (y). A one-to-one function is a special type of function where each input maps to a unique output (no repeats!)

11. Relations and Functions
Relation – a mapping of input values (x-values) onto output values (y-values).
Here are 3 ways to show the same relation.
x y
y = x2
Equation
Table of values
Graph

12. Inverse relation – just think: switch the x & y-values.-2 -1
x = y2
** the inverse of an equation: switch the x & y and solve for y.
** the inverse of a table: switch the x & y.
** the inverse of a graph: the reflection of the original graph in the line y = x.

13. Graph f(x) and f -1(x) on the same graph.-4 5 5 -4 3 3 4 5 5 4

14. Graph f(x) and f -1(x) on the same graph.-4 -4 -4 -4 -3 -5 -5 -3 4 4

15. Let’s consider the function and compute some values and graph them.
Notice that the x and y values traded places for the function and its inverse.
These functions are reflections of each other about the line y = x
Let’s consider the function and compute some values and graph them.
This means “inverse function”
x f (x)
(2,8)
(8,2)
x f -1(x)
Let’s take the values we got out of the function and put them into the inverse function and plot them
(-8,-2)
(-2,-8)
Is this a function?
Yes
What will “undo” a cube?
A cube root