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, stretching, compressing, or reflecting.

Front

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

Back

Reflecting a function 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 a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

How does a horizontal shift affect a function?

Back

A horizontal shift moves the graph of a function left or right along the x-axis. A positive shift moves it to the right, while a negative shift moves it to the left.

Front

What is the effect of a vertical translation on a function?

Back

A vertical translation moves the graph of a function up or down. Adding a constant moves it up, while subtracting a constant moves it down.

Front

What does it mean to reflect a function over the y-axis?

Back

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

Front

What transformation occurs when a function is multiplied by a negative number?

Back

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

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is y = |x|.