Linear transformations on Graphs

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

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Back

This represents a reflection of the function f across the y-axis.

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Back

This represents a vertical compression of the function f by a factor of 1/2 and a reflection across the x-axis.

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Back

This represents a vertical shift of the function f downwards by 5 units.

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Back

This represents a vertical shift of the function f upwards by 5 units.

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Back

This represents a vertical stretch of the function f by a factor of 2.

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Back

This represents a horizontal compression of the function f by a factor of 1/2 and a reflection across the y-axis.

Front

What is the effect of multiplying a function by a negative scalar?

Back

It reflects the function across the x-axis.

Front

What is the effect of adding a constant to a function?

Back

It shifts the graph of the function vertically.

Front

What is the effect of multiplying a function by a positive scalar greater than 1?

Back

It stretches the graph of the function vertically.