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

Back

A reflection over the x-axis transforms f(x) into -f(x), flipping the graph upside down.

Front

What is the effect of multiplying a function by a factor greater than 1?

Back

Multiplying a function by a factor greater than 1 vertically stretches the graph away from the x-axis.

Front

What happens when a function is multiplied by a factor between 0 and 1?

Back

Multiplying a function by a factor between 0 and 1 vertically shrinks the graph towards the x-axis.

Front

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

Back

The notation f(x + c) represents a horizontal shift of the graph to the left by c units.

Front

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

Back

The notation f(x - c) represents a horizontal shift of the graph to the right by c units.

Front

How does the transformation g(x) = f(x) + k affect the graph?

Back

The transformation g(x) = f(x) + k shifts the graph vertically by k units; up if k is positive and down if k is negative.

Front

What is the effect of the transformation g(x) = f(2x)?

Back

The transformation g(x) = f(2x) compresses the graph horizontally by a factor of 2.