Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does a vertical shift of a function do?

Back

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

Front

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

Back

A horizontal shift moves the graph of the function left or right.

Front

What does the notation f(x - h) represent?

Back

It represents a horizontal shift of the graph of f(x) to the right by h units.

Front

What does the notation f(x + h) represent?

Back

It represents a horizontal shift of the graph of f(x) to the left by h units.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis flips the graph of the function over the x-axis, changing the sign of the output values.

Front

What is a reflection in the y-axis?

Back

A reflection in the y-axis flips the graph of the function over the y-axis, changing the sign of the input values.

Front

What does a vertical stretch do to a function?

Back

A vertical stretch increases the distance of the graph from the x-axis, making it taller.

Front

What does a vertical compression do to a function?

Back

A vertical compression decreases the distance of the graph from the x-axis, making it shorter.

Front

What is the effect of the transformation f(-x)?

Back

The transformation f(-x) reflects the graph of the function over the y-axis.