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, which retains the essential characteristics of that family.

Front

What is the parent function of a quadratic equation?

Back

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

Front

How does a vertical shift affect the graph of a function?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

What does a horizontal shift do to the graph of a function?

Back

A horizontal shift moves the graph left or right without changing its shape.

Front

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

Back

A reflection over the x-axis flips the graph of the function upside down.

Front

What is the effect of a reflection over the y-axis on a function?

Back

A reflection over the y-axis flips the graph of the function horizontally.

Front

What does a vertical stretch by a factor of 2 do to the graph of a function?

Back

A vertical stretch by a factor of 2 makes the graph taller, increasing the distance from the x-axis.

Front

What does a horizontal compression by a factor of 2 do to the graph of a function?

Back

A horizontal compression by a factor of 2 makes the graph narrower, decreasing the distance between points on the x-axis.

Front

How do you translate the graph of f(x) = x² left 4 units?

Back

To translate left 4 units, use the equation f(x) = (x + 4)².

Front

How do you reflect the graph of f(x) = x² over the x-axis?

Back

To reflect over the x-axis, use the equation f(x) = -x².