Transformations of Functions

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

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 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 is a horizontal stretch of a function?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider.

Front

What is a horizontal compression of a function?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor between 0 and 1, making the graph narrower.

Front

How does a vertical translation affect a function?

Back

A vertical translation shifts the graph of a function up or down without changing its shape.

Front

How does a horizontal translation affect a function?

Back

A horizontal translation shifts the graph of a function left or right without changing its shape.

Front

What is the parent function of y = x^2?

Back

The parent function of y = x^2 is the simplest form of a quadratic function, which is a parabola opening upwards.

Front

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

Back

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