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 parent function of linear transformations?

Back

The parent function of linear transformations is f(x) = x.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up means adding a positive constant to the function, while shifting it down means subtracting a constant.

Front

If g(x) = f(x) + k, what does k represent?

Back

k represents a vertical shift; if k is positive, the graph shifts up, and if k is negative, it shifts down.

Front

What does a vertical stretch by a factor of a > 1 do to the graph of a function?

Back

A vertical stretch by a factor of a > 1 makes the graph steeper.

Front

What does a vertical compression by a factor of 0 < a < 1 do to the graph of a function?

Back

A vertical compression by a factor of 0 < a < 1 makes the graph less steep.

Front

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

Back

A horizontal shift moves the graph left or right; g(x) = f(x - h) shifts right by h units, and g(x) = f(x + h) shifts left by h units.

Front

What does it mean for a graph to be less steep?

Back

A graph is less steep when its slope is smaller, indicating that it rises or falls more gradually.

Front

What is the effect of a reflection over the x-axis on a function?

Back

A reflection over the x-axis changes the sign of the output values, resulting in g(x) = -f(x).

Front

How do you describe a transformation that results in g(x) = 2f(x)?

Back

This transformation represents a vertical stretch by a factor of 2.