parent functions and transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, representing the basic shape of the graph.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

What transformation occurs when a function is shifted up by k units?

Back

The transformation is represented as y = f(x) + k.

Front

What transformation occurs when a function is shifted down by k units?

Back

The transformation is represented as y = f(x) - k.

Front

What transformation occurs when a function is shifted left by h units?

Back

The transformation is represented as y = f(x + h).

Front

What transformation occurs when a function is shifted right by h units?

Back

The transformation is represented as y = f(x - h).

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means to invert the y-values, represented as y = -f(x).

Front

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

Back

Reflecting a graph over the y-axis means to invert the x-values, represented as y = f(-x).

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, making the graph taller.

Front

What is the effect of a vertical compression on a function?

Back

A vertical compression occurs when the function is multiplied by a factor between 0 and 1, making the graph shorter.