# Precalculus Examples

The parent function is the simplest form of the type of function given.

The slope-intercept form is , where is the slope and is the y-intercept.

Using the slope-intercept form, find the y-intercept for .

Using the slope-intercept form, find the y-intercept for .

List the y-intercepts.

The vertical shift depends on the y-intercept value , where

Since , the graph is shifted down units.

Shifted down units

The slope-intercept form is , where is the slope and is the y-intercept.

Using the slope-intercept form, find the slope for .

Using the slope-intercept form, find the slope for .

List the slopes.

The vertical stretch depends on the slope.

If , vertical compression

If , vertical stretch

If , no vertical stretch or compression.

Since , the graph is vertically stretched.

Vertical stretch

Since and do not have opposite signs, the graph is not reflected about the y-axis.

Not reflected about the y-axis

Describe the transformation from the function .

Shifted down units

Vertical stretch