Vertex Form of Absolute Value

Absolute Value Functions - Tables

Absolute Value Function is written as f(x)= |x|. The graph looks like a V; the turning point is called the vertex.

Multiple Choice

Which of the following is the graph of an absolute function?

Multiple Choice

Which equation represents the following table?

• f(x) = |3x-6|+1

• f(x)= |x| - 4

• f(x)=|x+1| - 2

• f(x) = |x-2|+1

Multiple Choice

Which equation represents the following table?

• f(x) = |3x-6|+1

• f(x)= |x| - 4

• f(x)=|x+1| - 2

• f(x) = |x-2|+1

Multiple Choice

Which equation represents the following table?

• f(x) = |3x-6|+1

• f(x)= |x+2|

• f(x)=|x+1| - 2

• f(x) = |2x+6|-3

Multiple Choice

Which equation represents the following table?

• f(x) = |x-2|+1

• f(x) = |3x-6|+1

• f(x)=|x+1| - 2

• f(x) = |2x+6|-3

Multiple Choice

Which table represents the following function f(x)=|x+1| - 2

Multiple Choice

Which function is graphed?

• f(x) = -|2x - 3| + 5
• f(x) = -|x + 5| - 3
• f(x) = -|2x + 6| + 5
• f(x) = -2|x + 5| - 3

Multiple Choice

Which function is graphed?

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

Graphing Absolute Value Functions with Transformations

PARENT FUNCTION

Parameters a, h, k

a- slope

h-left or right

k-up or down

Parameters of the Absolute Value Function:

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

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

• 4

• 2

Open Ended

What is the value of k?

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

Okay, let's take a look at this graph!

Multiple Choice

Which function defines the graph?

• f(x) = |x - 4| + 3

• f(x) = |x - 3| + 4

• f(x) = |-x + 4| + 3

• f(x) = |x + 4| + 3

Multiple Select

What is the equation of the graph below?

• f(x ) = I x + 4 I + 2

• f(x ) = I x - 4 I + 2

• f(x ) = -I x - 4 I + 2

• f(x ) = -I x + 4 I + 2

Multiple Choice

Write an absolute value function given the following transformations:

Vertical Stretch of 2

Horizontal shift left 1 unit

Vertical shift down 9 units

• f(x) = |2x + 1| - 9

• f(x) = |2x - 1| - 9

• f(x) = 2|x + 1| - 9

• f(x) = 2|x - 1| - 9

Multiple Select

What is the equation of the graph below?

• y = - | x + 2| + 4

• y = | x - 2| - 4

• y = - | x - 2| + 4

• y = | x - 2 | + 4

Open Ended

Describe in words how the graph transformed.

Multiple Choice

What is the equation of the absolute value function?

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

Multiple Choice

  . 
The blue graphs is the parent function f(x)=|x|, the red must be

• g(x)=|x+2|
• g(x)=|x|+2
• g(x)=|x-2|
• g(x)=|x|-2

Multiple Choice

Which function shows horizontal translation and a vertical stretch?

• f(x) = -2|-x | 
• f(x) = -3|x| - 7
• f(x) = -|-x + 1| + 4
• f(x) = 5|x - 4| - 1

Multiple Choice

Which function is graphed?

• f(x) = -3|-x + 1| + 4
• f(x) = -|x - 1| + 4
• f(x) = -5|x + 1| + 4
• f(x) = -3|x - 4| + 1