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More Lessons on Pre-Calculus

Transformations of Trigonometric Graphs

Examples, videos, worksheets, solutions, and activities to help PreCalculus students learn about horizontal and vertical graph stretches and compressions.

The following table gives a summary of the Transformation Rules for Graphs. Scroll down the page for more examples, solutions and explanations.

**Function Transformations: Horizontal and Vertical Translations**

This video explains to graph graph horizontal and vertical translation in the form af(b(x-c))+d.

It looks at how c and d affect the graph of f(x).

**Function Transformations: Horizontal and Vertical Stretch and Compression**

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

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

**Horizontal And Vertical Graph Stretches and Compressions. (Part 1)**

The general formula is given as well as a few concrete examples.

y = c f(x), vertical stretch, factor of c

y = (1/c) f(x), compress vertically, factor of c

y = f(cx), compress horizontally, factor of c

y = f(x/c), stretch horizontally, factor of c

y = - f(x), reflect at x-axis

y = f(-x), reflect at y-axis**Horizontal and Vertical Graph Stretches and Compressions. (Part 2)**

This video discusses the horizontal stretching and compressing of graphs.

**Graph Transformations about the X-axis and Y-axis**

This video talks about reflections around the X axis and Y axis.(Part 3)

**Effects on the parent function**

In this video we discuss the effects on the parent function when:

Stretched Vertically,

Compressed Vertically,

Stretched Horizontally,

Compressed Horizontally.

**Different types of math transformation**

There are different types of math transformation, one of which is the type y = f(bx). This type of math transformation is a horizontal compression when b is greater than one. We can graph this math transformation by using tables to transform the original elementary function. Other important transformations include vertical shifts, horizontal shifts, and reflections.

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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons on Pre-Calculus

Transformations of Trigonometric Graphs

Examples, videos, worksheets, solutions, and activities to help PreCalculus students learn about horizontal and vertical graph stretches and compressions.

The following table gives a summary of the Transformation Rules for Graphs. Scroll down the page for more examples, solutions and explanations.

This video explains to graph graph horizontal and vertical translation in the form af(b(x-c))+d.

It looks at how c and d affect the graph of f(x).

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

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

The general formula is given as well as a few concrete examples.

y = c f(x), vertical stretch, factor of c

y = (1/c) f(x), compress vertically, factor of c

y = f(cx), compress horizontally, factor of c

y = f(x/c), stretch horizontally, factor of c

y = - f(x), reflect at x-axis

y = f(-x), reflect at y-axis

This video discusses the horizontal stretching and compressing of graphs.

This video talks about reflections around the X axis and Y axis.(Part 3)

In this video we discuss the effects on the parent function when:

Stretched Vertically,

Compressed Vertically,

Stretched Horizontally,

Compressed Horizontally.

There are different types of math transformation, one of which is the type y = f(bx). This type of math transformation is a horizontal compression when b is greater than one. We can graph this math transformation by using tables to transform the original elementary function. Other important transformations include vertical shifts, horizontal shifts, and reflections.

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

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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