Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is a change made to the function's graph that alters its position, shape, or size.

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 does a horizontal shift of a function do?

Back

A horizontal shift moves the graph of the function left or right without changing its shape.

Front

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

Back

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

Front

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

Back

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

Front

What does a vertical stretch do to a function?

Back

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

Front

What does a vertical compression do to a function?

Back

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

Front

What does a horizontal stretch do to a function?

Back

A horizontal stretch increases the distance between points on the graph and the y-axis, making the graph wider.

Front

What does a horizontal compression do to a function?

Back

A horizontal compression decreases the distance between points on the graph and the y-axis, making the graph narrower.

Front

If f(x) = x^2, what is g(x) = f(x + 2)?

Back

g(x) = (x + 2)^2, which shifts the graph of f(x) left by 2 units.