Linear Transformations

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What is a linear transformation?

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

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What happens to the graph of a function when you add a constant to it?

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Adding a constant shifts the graph vertically. If you add a positive constant, the graph shifts up; if you add a negative constant, it shifts down.

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What does it mean when a function is flipped over the x-axis?

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

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Multiplying a function by a negative number reflects the graph over the x-axis.

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