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 can be transformed to create other functions.

Front

How does the equation y = f(x - 4) transform the parent function?

Back

It shifts the graph of the parent function to the right by 4 units.

Front

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

Back

It reflects the graph of the function over the x-axis.

Front

What is the effect of adding a constant to the function, such as in y = f(x) + 2?

Back

It shifts the graph of the function upward by 2 units.

Front

What does the transformation y = f(x + 3) represent?

Back

It shifts the graph of the parent function to the left by 3 units.

Front

How does the equation y = -f(x) affect the graph of the parent function?

Back

It reflects the graph over the x-axis.

Front

What is a vertical stretch in the context of function transformations?

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 does a horizontal compression by a factor of 2 look like in function notation?

Back

It is represented as y = f(2x), which compresses the graph horizontally.

Front

What transformation does the equation y = f(1/2x) represent?

Back

It represents a horizontal stretch by a factor of 2.

Front

What is the effect of subtracting a constant from the function, such as in y = f(x) - 4?

Back

It shifts the graph of the function downward by 4 units.