1) Reflections of functions f(x) over the x-axis or y-axis produce new equations by changing the sign of the y-values or x-values respectively. 2) The inverse of a function f(x) is denoted f^-1(x) and is found by switching the x and y values when graphed, effectively reflecting over the line y=x. 3) For example, the inverse of f(x)=2x+5 is found by graphing f^-1(x) which treats x as the output and y as the input.

1. Exercise #9
Symmetry, Reflections and Inverses
Reflections
f ( x)
y
x
f ( x)
f ( x)
Example
Given f ( x) 3x 4 , write an equation formed by reflecting f ( x) over the:
a) x-axis
b) y-axis
Graph each equation.
y
x
Homework Exercise 9 #1, 3, 7, 9, 11, 12, 14

2. Inverse
Inverse functions are denoted by f 1 ( x) .
Example
Given f ( x) 2 x 5 , graph f 1 ( x) .
To graph or find the inverse of
f ( x) , switch the x and y values.
Basically, when graphing the inverse of a function, f ( x) is reflected over the line y x
OR choose points and switch the x and the y values around.
y
x
Example
Given the graph of f ( x) below, sketch the graph of f 1 ( x) .
y
x
Homework Exercise 9 #2, 8, 13, 16, 18, 19