More Lessons for PreCalculus

Math Worksheets

Videos, worksheets, games and activities to help PreCalculus students learn about horizontal and vertical graph transformations.

Vertical Stretch and Vertical Compression

y = af(x), a > 1, will stretch the graph f(x) vertically by a factor of a.

y = af(x), 0 < a < 1, will stretch the graph f(x) vertically by a factor of a.

Horizontal Stretch and Horizontal Compression

y = f(bx), b > 1, will compress the graph f(x) horizontally.

y = f(bx), 0 < b < 1, will stretch the graph f(x) horizontally.

Horizontal Shift

y = f(x + c), will shift f(x) left c units.

y = f(x - c), will shift f(x) right c units.

Vertical Shift

y = f(x) + d, will shift f(x) up d units.

y = f(x) - d, will shift f(x) down d units.

Function Transformations: Horizontal and Vertical Stretches and Compressions

This video explains how to graph horizontal and vertical stretches and compressions in the form a×f(b(x-c))+d.

This video looks at how a and b affect the graph of f(x).

This video explains how to graph horizontal and vertical translation in the form a*f(b(x-c))+d. This video looks at how c and d affect the graph of f(x).

This video reviews function transformation including stretches, compressions, shifts left, shifts right, and reflections across the x and y axes.

9 full examples as well as the basic outline of doing horizontal and vertical translations of graphs are shown.

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