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, reflecting, stretching, or compressing.

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions in the same family can be derived through transformations.

Front

What does it mean to translate a function?

Back

To translate a function means to shift its graph horizontally and/or vertically without changing its shape.

Front

What is a vertical stretch?

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?

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

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

Back

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

Front

What is the effect of shifting a function left or right?

Back

Shifting a function left or right involves adding or subtracting a value from the input variable (x) in the function's equation.

Front

What does it mean to shift a function up or down?

Back

Shifting a function up or down involves adding or subtracting a value from the output variable (f(x)) in the function's equation.

Front

What is the transformation for g(x) = f(x) + k?

Back

The transformation for g(x) = f(x) + k is a vertical shift of the graph of f(x) upward by k units if k > 0, and downward by k units if k < 0.

Front

What is the transformation for g(x) = f(x - h)?

Back

The transformation for g(x) = f(x - h) is a horizontal shift of the graph of f(x) to the right by h units if h > 0, and to the left by h units if h < 0.