Precalculus Examples

Describe the Transformation
The parent function is the simplest form of the type of function given.
Find the y-intercepts.
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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
Find the slopes.
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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
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