Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the position, size, or shape of its graph.

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 a horizontal shift in function transformations?

Back

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

Front

What does a reflection over the x-axis do to a function?

Back

A reflection over the x-axis flips the graph of the function upside down.

Front

What does a reflection over the y-axis do to a function?

Back

A reflection over the y-axis flips the graph of the function horizontally.

Front

What is a vertical stretch of a function?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

Front

What is a vertical shrink of a function?

Back

A vertical shrink decreases the distance between points on the graph and the x-axis, making the graph shorter.

Front

How do you represent a shift of a function f(x) to the right by 3 units?

Back

You represent it as f(x - 3).

Front

How do you represent a shift of a function f(x) up by 5 units?

Back

You represent it as f(x) + 5.

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.