Lesson # 3: Relections

Rules for x and y-axis:

For y = f(x) to go to y = f(-x), the graph of f(x) is reflected over the y-axis. In other words, x is replaced by -x.
For y = f(x) to go to -y = f(x), the graph of y = f(x) is reflected over the x-axis. In other words, y is replaced by -y.

Examples of basic equations:

1) y = (-x)^2 is the same as y = x^2, but it reflects over the y-axis.
2) y = -(x^2) is the same as y = x^2, but it refelcts over the x-axis.
3) y = 1/x is the same as y = 1/-x, but it reflects over the y-axis.
4) -y = *root*(16-x^2) is the same as y = *root*(16-x^2), but it reflects over the x-axis.

Rules for Inverses:     *An inverse is the reflection across the line y = x.*

1) Swap x and y                 y = f(x) goes to y = f^-1(x)
2) Isolate y
3) rewrite f^-1(x)

Example:               *Find f^-1(x)*
f(x) = -1/2x+3
x = -1/2x+3
(Multiply everything by 2)
2x = -y+6
y = -2x+6
f^-1(x) = -2x+6     *Remember that y = f(x) and f^-1(x) and NOT 1/f(x)*