# CHARACTERSTICS OF ABSOLUTE VALUE FUNCTIONS WORKSHEET

Find the following and graph it.

(i) Vertex

(ii)  Slope

(iii) y-intercept and x-intercept

(iv) domain and range

(v)  Increasing and decreasing interval.

Problem 1 :

f(x) = -3│x - 4│ + 3

Solution

Problem 2 :

f(x) = -1/2│x - 2│ + 4

Problem 3 :

f(x) = │x - 3│ - 2

Problem 4 :

f(x) = 3│x│

Problem 5 :

y = 3/5 │x│- 6

Problem 6 :

y =│x + 4│

1)

2)

3)

4)

5)

6)

Graph the following absolute value function by finding the following.

(i) Vertex

(ii)  Slope

(iii)  Direction of opening

(iv) x and y intercepts

(v) Domain and range

(vi) Increasing and decreasing

Problem 1 :

y = 3|x - 3|

Solution

Problem 2 :

y = -|x| + 4

Problem 3 :

y = (4/3) |x + 2| - 5

Problem 4 :

y = -(3/2) |x - 3| + 2

1)  Vertex is at (3, 0)

Slope (a) = 3

Direction of opening = open up

x-intercept is at (3, 0)

y-intercept is at (0, 9).

• All real values is domain.
• Range is 3 ≤ y ≤ ∞
• To the left of minimum, it is decreasing.
• To the right of minimum, it is increasing.

2)  Vertex is at (0, 4).

x-intercepts are (4, 0) and (-4, 0).

y-intercept is at (0, 4).

Slope (a) = -1

The curve will open down.

• All real values is domain.
• Range is 4 ≤ y ≤ -∞
• To the left of maximum, it is increasing.
• To the right of maximum, it is decreasing.

3)  Vertex is at (-2, -5).

x-intercept is at (7/4, 0) and (-19/2, 0).

y-intercept (0, -7/3).

Slope (a) = 4/3

The curve will open up.

• All real values is domain.
• Range is 4 ≤ y ≤ -∞
• To the left of minimum, it is decreasing.
• To the right of minimum, it is increasing.

4)  Vertex is at (3, 2).

x-intercept is at (13/3, 0) and (5/3, 0).

y-intercept is (0, -5/2).

Slope (a) = -3/2

The curve will open down.

• All real values is domain.
• Range is -5 ≤ y ≤ ∞
• To the left of maximum, it is increasing.
• To the right of maximum, it is decreasing.

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