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 does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

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

Back

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

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means adding or subtracting a constant from the function, which moves the graph up or down without changing its shape.

Front

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

Back

Multiplying a function by a scalar greater than 1 stretches the graph vertically, making it steeper.

Front

What is the effect of multiplying a function by a scalar between 0 and 1?

Back

Multiplying a function by a scalar between 0 and 1 compresses the graph vertically, making it less steep.

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Back

Front

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

Back

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Front

What is the relationship between the slopes of two linear functions?

Back

The slope of a linear function indicates its steepness. If one function's slope is greater than another's, it is steeper.