PRACTICE WORKSHEET ON ABSOLUTE VALUE FUNCTIONS

Problem 1 :

What is the vertex: y = 3|x - 1| + 2

a) (1, -2)    b) (1, 2)

Solution

Problem 2 :

What is the vertex: y = 2|x|

a) (2, 0)    b) (0, 0)

Solution

Problem 3 :

What is the vertex: y = |x| + 5

a) (5, 0)    b) (0, 5)

Solution

Problem 4 :

The graph of y = -2|x + 1| - 3 is

a) Vertically stretched   b) Vertical shrink

Solution

Problem 5 :

The graph of y = -3/5|x + 3| + 10 is

a) Vertically stretched   b) Vertical shrink

Solution

Problem 6 :

The graph of y = 15|x| is

a) Vertically stretched   b) Vertical shrink

Solution

Problem 7 :

The graph of y = 5/3|x + 2| - 1 is

a) Vertically stretched   b) Vertical shrink

Solution

Problem 8 :

The graph of y = 5/3|x + 2| - 1

a) Opens up   b) Opens down

Solution

Problem 9 :

The graph of y = -2|x + 1| - 3

a) Opens up   b) Opens down

Solution

Problem 10 :

The graph of: y = 3|x| - 2 is

a) Translated vertically   b) Translated horizontally

Solution

Problem 11 :

The graph of: y = 3|x| - 2 is 

a) Translated left 2   b) Translated down 2

Solution

Problem 12 :

In order for the graph to be a vertical shrink, what will be the value of a

a)  -1 < a < 1       b) a > 1

Solution

Problem 13:

Domain of: y = -2|x + 1| - 3

a)  (-∞, ∞)       b) -∞ < x < 1

Solution

Problem 14 :

Range of: y = 3|x| - 1

a)  (-∞, 3]     b) [-1, ∞)

Solution

Problem 15 :

Range of: y = -|x| - 2

a)  [-2,-∞)     b) [-2, ∞)

Solution

Problem 16 :

Range of: y = -|x - 5| + 4

a)  (-∞, 4]     b) [4, ∞)

Solution

Problem 17 :

Let f(x) = ∣x − 3∣ − 5

Write

(a) a function g whose graph is a horizontal shrink of the graph of f by a factor of 1/3 , and

(b) a function h whose graph is a vertical stretch of the graph of f by a factor of 2.

Solution

Problem 18 :

Write a function g whose graph is a horizontal stretch of the graph of f(x) = ∣ x ∣ by a factor of 3, followed by a reflection in the y-axis.

Solution

Describe the translation from the graph of f(x) = ∣x - h∣ + k to the graph of the given function. Here (h, k) be (0, 0). Then graph the given function

Problem 1 :

f(x) = |x + 2| - 6

Solution

Problem 2 :

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

Solution

Problem 3 :

f(x) = |x - 3| + 5

Solution

Problem 4 :

f(x) = |x - 1| + 3

Solution

Problem 5 :

Describe and correct the error in graphing the function.

Solution

Problem 6 :

Compare the graphs. Find the value of h and k 

Solution

Problem 7 :

Compare the graphs. Find the value of h and k 

Solution

Problem 8 :

(i)  Vertical translation 7 units down.

(ii)  Horizontal translation 10 units left

Solution

Problem 9 :

Write a function g whose graph represents the indicated transformation of the graph of f.

f(x) = ∣4x + 3∣ + 2; translation 2 units down

Solution

Problem 10 :

Write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer.

f(x) = 4 − ∣x + 1|

Solution

Problem 11 :

Write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer.

f(x) = ∣4x∣ + 5

Solution

Problem 12 :

Write a function g whose graph represents the indicated transformations of the graph of f.

f(x) = ∣x∣ ; translation 2 units to the right followed by a horizontal stretch by a factor of 2

Solution

Answer Key

1) 

2)

3) 

4)

5) In the given graph, it is moved 3 units down. Instead of moving to the right, it is moved to the left. So, this is the error.

6) Vertical movement = -2 (since moving down)

7) 

horizontal movement = 1 unit

Vertical movement = 0

8) i)  y = |x| - 7

ii)  y = |x - 10|

9) f(x) = ∣4x + 3∣

10) f(x) = 4 − ∣x - 2|

11)  f(x) = ∣4x∣ + 6

12) f(x) = 2|x - 2|