Basic Shifting of Parent Functions (Using Absolute Value)

How to Move A Function

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

Multiple Choice

Which absolute value equation is the "parent function?"

• y = |x - 3|
• y = |x + 5|
• y = |x|
• y = |x + 2|

Multiple Choice

What color is the parent function in the graphs below?

• The red one

• The green one

• I don't know because I really didn't read the previous slides

Audio Response

Describe what a parent function is.

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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

Multiple Choice

Describe the vertical shift.

• Up 4

• Down 4

• Right 4

• Left 4

Multiple Choice

What is the equation of the red graph?

• y=|x|

• y=|x|+4

• y=|x|-4

• y=|x-4|

Multiple Choice

What is the equation of the green graph?

• y=|x|

• y=|x|+4

• y=|x|-4

• y=|x-4|

Multiple Choice

What is the equation of the green graph?

• y=|x|

• y=|x|+5

• y=|x|-5

• y=|x+5|

Note!

​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.

Video Response

Describe how a number added or subtracted to the end of a parent function equation changes the graph of the function. (Use hand motions to show what you are talking about).

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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"

Multiple Choice

What does "counter-intuitive" mean?

• The way you think it should be.

• Not understandable.

• Opposite the way you think it should be.

• The idea that we should have counters in the kitchen.

Multiple Choice

What does "intuitive" mean?

• The way you think it should be.

• Not understandable.

• Opposite the way you think it should be.

• The idea that we should have counters in the kitchen.

Multiple Choice

What type of shift is "intuitive?"

• Horizontal shift

• Manual shift

• Gear shift

• Vertical shift

Multiple Choice

What type of shift is "counter-intuitive?"

• Horizontal shift

• Manual shift

• Gear shift

• Vertical shift

Multiple Choice

What is the equation of the green graph?

• y = |x+2|

• y = |x-2|

• y = |x|+2

• Not enough information to determine the equation

Multiple Choice

What is the equation of the green graph?

• y = |x+6|

• y = |x|

• y = |x|+2

• y = |x-6|

Fill in the Blanks

Write the equation of the green graph? (no spaces)

Audio Response

Describe which kind of transformation is "counter-intuitive" and which type of transformation is "intuitive" when you are shifting a parent function.

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