1. Graph the function and it’s inverse On the same graph f(x) = 2x + 10
WARM UP
Graph the function and it’s inverse
On the same graph
f(x) = 2x + 10

2. How do you find the inverse of a function?
Math II Day 52 ( )
Standard MM2A5.a
Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.
Today’s Question:
How do you find the inverse of a function?

3. 4.3 Inverse Functions p

4. Review
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

5. 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.

6. y = 2x (1/2)x - 2 = y x y -5 -6 5 -2 1 6 2 8 14

7. Let’s inverse some bigger functions
Parabolas

8. No X can have more than one Y
To be a function……
No X can have more than one Y
Or No X can be repeated X Y 1 5 2 6 3 7 4 X Y 1 5 2 6 7 3 8 9

9. Vertical Line Test X Y 1 5 2 6 7 3 8 9 X Y 1 5 2 6 3 7 4

10. Vertical Line Test Used to determine whether a graph is a function.
If the original function passes the vertical line test, then a function.
If the original function does not pass the vertical line test, then it is not a function.

11. Ex: Graph the function f(x)=x2 and determine whether it is a function.
Graph passes the vertical line test, therefore it is a function.

12. Ex: Graph the function f(x)=x2 and determine whether it is a function.
Graph fails the vertical line test, therefore it is not a function.

13. Horizontal Line Test
Used to determine whether a function’s inverse will be a function by seeing if the original function passes the horizontal line test.
If the original function passes the horizontal line test, then its inverse is a function.
If the original function does not pass the horizontal line test, then its inverse is not a function.

14. Ex: Graph the function f(x)=x2 and determine whether its inverse is a function.
Graph does not pass the horizontal line test, therefore the inverse is not a function.

15. Ex: g(x)=2x3
Inverse is a function!

16. 4 Corners Stations Graph each function and it’s inverse
Tell if the inverse is a function

17. Homework
PG #1 – 6, 9, 10