Graphing Absolute Value Equations

Graphing Absolute Value Equations

Absolute Value Equations

• The absolute value equation is in the form

   $f\left(x\right)=a\cdot\left|b\cdot x-h\right|+k$  

• a, b, h, and k are all parameters that affect how the graph of an absolute equation looks along with the table of values generated by the function.

Parameters of the Absolute Value Function:

• a Compresses or stretches the graph vertically (Graph will Push TO and Pull AWAY from the X-axis)

• b Compresses or stretches the graph vertically (Graph will Push TO and Pull AWAY from the Y-axis)

• h Translates the graph of the absolute value function either to the left (+h) or right (-h) !

• k Translates the graph of the absolute value function either to the up (+k) or down (-k) !

Transformed Absolute Value Function (Red Graph) vs. Parent Absolute Value Function (Green Graph)

Copy and paste the link below to transform the graph of an absolute value function and compare it to the graph of the parent absolute value function.

https://www.geogebra.org/m/erepkave

Graph an Absolute Value Function

Adjust the parameters of the absolute value function to create specific absolute value equations.

Copy and Paste to view change parameters of an absolute value equation.

https://www.geogebra.org/m/z8zhgxbn

Absolute Value Functions

(Graph and describe transformations of an absolute value function)

Multiple Select

Select all that apply. (May have more than one correct answer)

f(x) = |x - 6| + 2

• Horizontal translation right 6 units

• Horizontal translation left 6 units

• Vertical translation up 2 units

• Vertical translation down 2 units

Multiple Choice

What is the value of h?

f(x) = |x + 4| - 2

• 4

• 2

• 1

• 0

Multiple Choice

What is the value of K?

f(x) = 4|x +2| - 3

• 4

• 2

• -3

• 0

Multiple Choice

What is the value of A?

f(x) = -2|x - 4| + 3

• -4

• 2

• -2

• 3

Multiple Choice

Which of the graphs given is

y=|x+1|−4 ?

(Click on the picture to enlarge it so you can see)

• A

• B

• C

• y=D

Multiple Choice

What function best describes this graph? (Click the picture to zoom in)

• f(x)= -|x+4| + 1

• f(x)= |x-1| + 4

• f(x)= |x+1| + 4

• f(x)= -|x+1| + 4

Multiple Choice

Which graph matches the function?

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

(Click the picture to zoom in and see the graphs up close!)

• A

• B

• C

• D

Multiple Choice

What is the equation of the graph below? You can click the picture to zoom in!

• y = - | x + 2| + 4

• y = - | x - 2| + 4

• y = | x - 2 | + 4

• y = | x - 2| - 4

Multiple Choice

What is the equation of the graph below?

(You can click the picture to zoom in!)

• f(x) = I x + 2 I

• f(x) = I x I + 2

• f(x) = I x I - 2

• f(x) = I x - 2 I

Multiple Choice

What is the graph of the equation y=|x+2|+1?

(Click the picture to see all the graphs up close)

• A

• B

• C

• D

Multiple Choice

What is the graph of y=|x−2|+3 ?

(Click the picture to see all the graphs)

• A

• B

• C

• D

Multiple Choice

What is the graph of y=|x|−2 ?

(Click the picture to see the graphs up close)

• A

• B

• C

• D