Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of a function, which can include shifts, reflections, stretches, and compressions.

Front

What does it mean to translate a function up?

Back

Translating a function up means shifting the entire graph of the function vertically in the positive y-direction by a certain number of units.

Front

What does it mean to translate a function down?

Back

Translating a function down means shifting the entire graph of the function vertically in the negative y-direction by a certain number of units.

Front

What is the effect of shifting a function to the right?

Back

Shifting a function to the right means moving the graph horizontally in the positive x-direction by a certain number of units.

Front

What is the effect of shifting a function to the left?

Back

Shifting a function to the left means moving the graph horizontally in the negative x-direction by a certain number of units.

Front

How do you reflect a function over the x-axis?

Back

To reflect a function over the x-axis, you multiply the output of the function by -1, changing the sign of all y-values.

Front

How do you reflect a function over the y-axis?

Back

To reflect a function over the y-axis, you replace x with -x in the function's equation.

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 is a horizontal stretch of a function?

Back

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