Transformations & 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 retains the essential characteristics of that family.

Front

What effect does a vertical stretch have on a function?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

Front

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

Back

A vertical shrink decreases the distance between points on the graph and the x-axis, making the graph shorter.

Front

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

Back

A negative sign reflects the graph across the x-axis.

Front

What does a horizontal shift to the left mean for a function?

Back

A horizontal shift to the left means that every point on the graph moves left by a specified number of units.

Front

What does a horizontal shift to the right mean for a function?

Back

A horizontal shift to the right means that every point on the graph moves right by a specified number of units.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function results in a vertical shift of the graph up or down, depending on the sign of the constant.

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

How does the function f(x) = 5(x + 3)² - 10 transform the parent function?

Back

It vertically stretches the graph by a factor of 5, shifts it left 3 units, and shifts it down 10 units.