Basic Shifting of Parent Functions (Using Absolute Value)

A parent graph is the one that is simplest to write and is usually located at the center of the coordinate plane.

​The red graph is called a "parent graph."

​Notice that the green graph has a +2 at the end. It's more complex to write.

Notice that the green graph is not centered in the middle of the coordinate plane. It is shifted up 2 spaces.

​​The red graph: y=|x|
The green graph: y=|x|+2

When we shift any function up or down, it is called a vertical shift. Here, the parent function is shifted up 5 spaces to make the green function. ​Adding a number outside the absolute value bars, shifts the graph up.

The red graph: y = |x|
The green graph: y = |x|+5

Vertical Shift

​A vertical shift is intuitive.

"Intuitive" means "it functions exactly how you would guess it does."

A positive number shifts the function up.

A negative number shifts the function down.

The equation for the green graph is: y = |x+6|

Notice that a plus 6 inside with the x moves the function left (toward the negative side of the number line).

​

​Shifting Left and Right.

​That means that it is opposite the way we would typically think about things. We might guess that y=|x+6| would move the parent function toward positive 6. But it moves it toward -6 instead.

Left and Right is "Counter-Intuitive"