Transformations of Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which serves as a reference point for transformations.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally, vertically, or both without changing its shape.

Front

How do you translate a quadratic function left by 4 units?

Back

To translate a quadratic function left by 4 units, replace x with (x + 4) in the function's equation.

Front

What is the effect of reflecting a function over the x-axis?

Back

Reflecting a function over the x-axis changes the sign of the output values (y-values) of the function.

Front

How do you shift a function up by 2 units?

Back

To shift a function up by 2 units, add 2 to the entire function's equation.

Front

What is the transformation represented by f(x) = (x - 3)^2 + 5?

Back

This represents a translation right 3 units and up 5 units from the parent function y = x^2.

Front

What does a negative sign in front of a quadratic function indicate?

Back

A negative sign indicates that the function is reflected over the x-axis.

Front

How do you identify a vertical compression in a function?

Back

A vertical compression occurs when the output values of the function are multiplied by a factor between 0 and 1.

Front

What is the transformation for f(x) = (x + 2)^2 - 4?

Back

This represents a translation left 2 units and down 4 units from the parent function y = x^2.

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means replacing x with -x in the function's equation.