Linear Transformations

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.

Front

What is the standard form of a linear function?

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What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much the output value changes for a unit change in the input value.

Front

What is the y-intercept of a linear function?

Back

Front

How does a vertical stretch affect a linear function?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph steeper.

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How does a vertical compression affect a linear function?

Back

A vertical compression multiplies the output of the function by a factor between 0 and 1, making the graph less steep.

Front

What is a reflection in the context of linear transformations?

Back

A reflection is a transformation that flips a graph over a specified line, such as the x-axis or y-axis.

Front

What is the effect of a horizontal shift on a linear function?

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A horizontal shift moves the graph of the function left or right without changing its shape.

Front

What is the effect of a vertical shift on a linear function?

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A vertical shift moves the graph of the function up or down without changing its slope.

Front

What is the parent function of linear functions?

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