1. Inverse Relations and Functions

2. What do you notice about the graphs?
Using a graphing calculator, graph the pairs of equations on the same graph. Sketch your results.
These graphs are said to be inverses of each other.
What do you notice about the graphs?

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)
Function f(x)
Inverse of Function f(x) X Y 3 1 4 -3 -5 2 5 -8 X Y 3 4 1 -3 2 -5 5 -8

4. Let’s look at our graphs from earlier
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=x2+3
x=y2+3
x – 3 = y2
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. The Vertical Line Test
It can only be a function if there is only one y-value for each x-value
If the vertical line passes through at more than one point on the graph, it is NOT a function
You can tell if the inverse will be a function if it passes a horizontal line test

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

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

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