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 horizontal translation of a function do?

Back

A horizontal translation shifts the graph of the function left or right along the x-axis.

Front

What does a vertical translation of a function do?

Back

A vertical translation shifts the graph of the function up or down along the y-axis.

Front

What is the effect of a negative sign in front of a function, such as -f(x)?

Back

A negative sign reflects the graph of the function across the x-axis.

Front

What is the Absolute Value Parent function?

Back

Front

How does the function g(x) = f(x - 1) transform f(x)?

Back

The function g(x) translates f(x) to the right by 1 unit.

Front

How does the function g(x) = f(x) + 3 transform f(x)?

Back

The function g(x) translates f(x) upward by 3 units.

Front

What is a vertical stretch of a function?

Back

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

Front

What does the transformation g(x) = 4f(x) represent?

Back

The transformation g(x) = 4f(x) represents a vertical stretch of the function f(x) by a factor of 4.