Lesson 3 - Reflections

Rules for x and y axis:

 For y= f(x) to y= f(-x) , the graph of f(x) is reflected over the y-axis. Algebraically, x is replaced with - x.

 For y= f(x) to -y + f(x), the graph will reflect over the x-axis. Algebraically, y is replaced with -y.


 Relations between basic equations:

y= (-x)^2  is the same as y= x^2 but will reflect over the y-axis.
y= -(x^2) is the same as -y= x^2 and will reflect over the x-axis.
y= 1/ -x is the same as y= 1/x and reflects over the y-axis.
y= square root of 16 - x^2 which reflects over the x-axis.

Inverses:

An inverse is the reflection across the line y = x
Rules:
1) swap x to y
2) isolate y
3) rewrite f ^-1(x)

The notations:
y= f(x)  goes to y= f ^ -1 (x)

example: 
f(x)= -1/2x + 3
Find f^-1(x)
x= -1/2y +3
multiply everything by 2
2x= -y + 6
y= -2x + 6
f^-1 = -2x +6