Unit 4: Constructing Functions

You'll how define a relationship between inputs and outputs, which involves using transformation.

Vertical translation

A transformation that moves a graph up or down along the y-axis, changing only its position and not its shape or orientation

Horizontal translation

Shifts a graph left or right along the x-axis, without changing its shape

Vertical dilation

A transformation that stretches or compresses a function vertically, changing the y-values without altering the x-values.This is done by multiplying the entire function by a constant factor, k. If k>1, the graph stretches vertically; if 0<k<1, it compresses vertically; and if k is negative, it reflects across the x-axis and then dilates

Horizontal dilation

a transformation that stretches or compresses a graph along the x-axis.It changes a function y=f(x) to y=f(kx), where the scale factor is \(1/k\). If \(k>1\), the graph is compressed horizontally; if 0<k<1, the graph is stretched horizontally.