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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.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.