Absolute Value Function Transformations

Transformations of Absolute Value Functions

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y = a |x - h| + k

• If "a" is positive the function opens up

• If "a" is negative, it is a reflection, meaning it opens down

• "a" is the slope of the branches of the graph

• The larger the "a" value, the more narrow it is

y = a |x - h| + k

• "h" is a horizontal translation

• if |x - h| move the graph to the right "h" units

• if | x + h| move the graph to the left "h" units

y = a |x - h| + k

• "k" is a vertical translation

• if "k" is positive it moves up

• if "k" is negative it moves down

Vertex

• either the highest or the lowest point on the graph

• has the coordinates (-h, k) the opposite of h and k

• 
  

Identify the vertex... y = |x - 3| + 7

• h = -3

• k = 7

• vertex (-h, K)

• The vertex is located at (3, 7)

Identify the transformations from the parent function y = |x| for the following function: y = -2|x + 7| - 3

• reflection

• slope is 2

• horizontal translation 7 units left

• vertical translation 3 units down

To write the function for the graph:

(For the parent function, the vertex is at the origin, opening up, with a slope of 1)

• Identify "a", "h" and "k"

• plug those values into y = a |x - h| + k

• 
  

• 
  

Multiple Choice

What function best describes this graph?

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

Multiple Choice

Identify the equation of the graph.

• y = - |x-1 | +1
• y = - |x+1| - 1
• y = |x-1| - 1
• y = -|x-1|-1

Multiple Choice

Identify the equation of the graph.

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

Multiple Choice

Identify the equation of the graph.

• y = |x - 1| - 1
• y = |x + 1| - 1
• y = |x - 1| +1
• y = |x + 1| + 1

Multiple Choice

Identify the equation of the graph.

• y = - | x + 2| + 4
• y = - | x - 2| + 4
• y = | x - 2 | + 4
• y = | x - 2| - 4

Multiple Choice

Which graph matches the function:
y = -2|x - 3| + 5

• A
• B
• C
• D

Multiple Choice

y = |x - 3| makes the graph slide . . .

• left 3
• right 3
• up 3
• down 3

Multiple Choice

y = |x| - 7 makes the graph slide . . .

• left 7
• right 7
• up 7
• down 7

Multiple Choice

Describe the transformation from the Absolute Value Parent Function.

• Shift up 4 units
• Shift down 4 units
• Shift left 4 units
• Shift right 4 units

Multiple Choice

Describe the transformation from the Absolute Value Parent Function.

• Shift up 4 units
• Shift down 4 units
• Shift left 4 units
• Shift right 4 units

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 vertex of the function?

f(x) = 2|x - 4|

• (2, -4)

• (2, 4)

• (-4, 0)

• (4, 0)

Multiple Choice

What is the vertex of the function?

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

• (-3, -2)

• (3, -2)

• (3, 2)

• (-3, 2)

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 h?

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

• 4

• 2

• 1

• 0

Multiple Select

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

Which letter(s) does the function have?

f(x) = 4|x-2|+1

• H

• A

• K

• None

Multiple Select

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

Which letter(s) does the function have? 

f(x) = -|x+3|

• H

• A

• K

• None