Absolute Value Functions and Equations

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.

• Absolute value does not always have to be positive.

• Absolute value is like a clock it has only positive numbers.

• Absolute value is talking about distance, distance is always measured by positive numbers.

What shifts have occurred?

• left 1, up 5

• left 1, down 5

• right 1, down 5

• right 1, up 5

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

• Left 4
  up 9

• Left 4
  Down 9

• Right 4
  up 9

• Right 4
  Down 9

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

What is the vertex of the absolute value function?

• (4, 0)

• (0, 4)

• (-infinity, infinity)

• [4, infinity)

What is the domain of the graph above?

• (-∞,∞)

• (-∞,2]

• [4,∞)

• [2,∞)

What is the domain of the graph above?

• (-∞,∞)

• (-∞,0]

• [0,∞)

• [2,∞)

What is the range of the graph above?

• (-∞,∞)

• (-∞,0]

• [0,∞)

• [2,∞)

Describe the transformations of the equation above:

• Stretches, shifts up 4 units

• Stretches, shifts down 4 units

• Shrinks, shifts up 4 units

• Shrinks, shifts down 4 units

Describe the transformations of the absolute value equation.

• reflection, shrinks, shifts right 1 unit

• reflection, shrinks, shifts up 1 unit

• reflection, stretches, shifts right 1 unit

• reflection, stretches, shifts up 1 unit