TRANSFORMATIONS OF FUNCTIONS

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 shrink of a function?

Back

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

Front

What does a horizontal stretch of a function mean?

Back

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

Front

What does a horizontal shrink of a function mean?

Back

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

Front

How do you shift a function to the right?

Back

To shift a function f(x) to the right by 'h' units, replace x with (x - h) in the function, resulting in f(x - h).

Front

How do you shift a function to the left?

Back

To shift a function f(x) to the left by 'h' units, replace x with (x + h) in the function, resulting in f(x + h).

Front

What is the transformation for g(x) = (x - 2)^2?

Back

This represents a horizontal shift of the function f(x) = x^2 to the right by 2 units.

Front

What is the transformation for g(x) = x^2 - 5?

Back

This represents a vertical shift of the function f(x) = x^2 downward by 5 units.

Front

What does g(x) = |x - 2| represent?

Back

This represents a horizontal shift of the function f(x) = |x| to the right by 2 units.

Front

What is the effect of multiplying a function by a negative factor?

Back

Multiplying a function by a negative factor reflects the graph across the x-axis.