Function Families & Transformations

Front

What is a function family?

Back

A group of functions that share common characteristics and can be represented by similar equations.

Front

What is a transformation in the context of functions?

Back

A change made to a function that alters its graph, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean for a function to be 'narrower'?

Back

A function is 'narrower' when it is stretched vertically, making it rise or fall more steeply.

Front

What does it mean for a function to be 'wider'?

Back

A function is 'wider' when it is compressed vertically, making it rise or fall less steeply.

Front

How does the equation f(x) = a(x - h)² + k affect the graph?

Back

The parameter 'a' affects the width and direction (upward or downward) of the parabola, 'h' shifts it horizontally, and 'k' shifts it vertically.

Front

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

Back

The output values (y-values) of the function are inverted, resulting in a graph that is a mirror image across the x-axis.

Front

What is the effect of reflecting a function across the y-axis?

Back

The input values (x-values) of the function are inverted, resulting in a graph that is a mirror image across the y-axis.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is f(x) = |x|.

Front

What does the notation f(-x) represent?

Back

It represents the reflection of the function f(x) across the y-axis.