1. Inverses Inverse Relations & Inverse Functions
What does it mean when two functions have an INVERSE relationship?

2. Activity
Get a partner
One person from the group get a piece of graph paper.
The other person get a piece of notebook paper.
Put BOTH of your names on both sheets.

3. Instructions
Plot the following points on your graph. Connect the points. x y -1 4 6 2 7 5 8 10

4. Now plot these points on your graph in the same coordinate plane
Now plot these points on your graph in the same coordinate plane. Connect the points. Then draw a dotted line for y=x. x y 4 -1 6 7 2 8 5 10

5. Questions What do you notice about the two graphs?
What do you notice about the points?
Do you think these points are inverse relationships? x y -1 4 6 2 7 5 8 10 x y 4 -1 6 7 2 8 5 10

6. Things you should notice: (facts about inverse relations/functions) Inverse relation – interchanges the input (x) values and output (y) values of the original relation Inverse relation graph – the result of reflecting the original graph over the line y=x

7. Finding inverse equations
Question: All equations should be in what form?
To find an inverse
Flip the x and y.
Solve for y.
Your resulting equation will be in the form: y-1=

8. Examples
y = 3x – 5
y = -x + 4

9. Note
When taking the square root, you get two answers: a positive and negative.
If given an f(x) function, do the same thing (flip x and y and solve). The answer will now be in f-1(x) form.
It needs to be renamed.

10. Examples
y = 4x2
f(x) = 8x – 2

11. Exit Ticket
What is the inverse relation for the following points? {(0, 6), (-1, 2), (3, 4), (-5, -3)}