TRANSLATION OF ABSOLUTE VALUE FUNCTIONS WORKSHEET

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

Write an equation that represents the given transformation(s) of the graph of g(x) = ∣x ∣ .

Problem 8 :

(i)  Vertical translation 7 units down.

(ii)  Horizontal translation 10 units left

Solution

Answer Key

1)

2)

3) 

4) 

5) Instead of moving to the right, it is moved to the left. So, this is the error.

6) horizontal movement = 0 units

Vertical movement = -2 (since moving down)

7) horizontal movement = 1 unit

Vertical movement = 0

8) (i)  Vertical translation (k) = -7 (down)

y = |x| - 7

(ii)  Horizontal translation (k) = 10 (left)

y = |x - 10|