# DOMAIN AND RANGE OF ABSOLUTE VALUE FUNCTIONS WORKSHEET

Find the domain and range of each function

Problem 1 :

y = |x|

Problem 2 :

y = -|x|

Solution

Problem 3 :

y = │x + 2│+ 3

Problem 4 :

y = │x│- 5

Problem 5 :

y = -│x│- 9

Problem 6 :

y = -│x - 3│+ 10

Solution

1)  Domain : (-∞, ∞), x  R and Range : [0, ∞), y ≥ 0

2)  Domain : (-∞, ∞), x  R and Range : [0, -∞), y ≤ 0

3)  Domain: (-∞, ∞), x  R and Range: [3, ∞), y ≥ 3

4) Domain: (-∞, ∞), x  R and Range: [-5, ∞), y ≥ -5

5)  Domain: (-∞, ∞), x  R and Range: [-9, -∞),  y ≤ -9

6)  Domain: (-∞, ∞), x  R and Range: [10, -∞), y ≤ 10

Write the equation of the graph. Then give its range as an inequality.

Problem 1 :

Problem 2 ::

Problem 3 :

Problem 4 :

Problem 5 :

Problem 6 :

Solution

 1)  y = 1 |x +1| + 2Range is 2 ≤ y ≤ ∞2)  y = -1 |x + 3| - 2Range is -2 ≤ y ≤ -∞3)  y = -2 |x - 2| + 3Range is 3 ≤ y ≤ -∞ 4)  y = (1/2) |x + 2| - 3Range is -3 ≤ y ≤ ∞5)  y = (-3/4) |x - 1|Range is 1 ≤ y ≤ -∞6)  y = (2/3) |x + 2|Range is -2 ≤ y ≤ ∞

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