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

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) 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|

9) f(x) = ∣4x + 3∣

10) f(x) = 4 − ∣x - 2|

11) f(x) = ∣4x∣ + 6

12) f(x) = 2|x - 2|

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

Problem 1 :

f(x) = x − 5; translation 4 units to the left

Solution

Problem 2 :

f(x) = x + 2; translation 2 units to the right

Solution

Problem 3 :

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

Solution

Problem 4 :

f(x) = 2x − 9; translation 6 units up

Solution

Problem 6 :

f(x) = 3x; translation 5 units up

Solution

Problem 7 :

f(x) = ∣x∣ − 3; translation 4 units to the right

Solution

Problem 8 :

f(x) = −∣x + 2 ∣ − 1; reflection in the x-axis

Solution

Problem 9 :

f(x) = (1/2) x + 1; reflection in the y-axis

Solution

Problem 10 :

f(x) = x; vertical stretch by a factor of 2 followed by a translation 1 unit up

Solution

Problem 11 :

f(x) = x; translation 3 units down followed by a vertical shrink by a factor of 1/3

Solution

Problem 12 :

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

Solution

Problem 13 :

f(x) = ∣x∣ ; reflection in the y-axis followed by a translation 3 units to the right

Solution

Problem 14 :

Let f(x) = 2x + 1

a. Write a function g whose graph is a translation 3 units down of the graph of f.

b. Write a function h whose graph is a translation 2 units to the left of the graph of f.

Solution

Problem 15 :

Let f(x) = ∣x + 3∣ + 1

a. Write a function g whose graph is a reflection in the x-axis of the graph of f.

b. Write a function h whose graph is a reflection in the y-axis of the graph of f.

Solution

Answer Key

1) g(x) = x - 1

2) g(x) = x

3)  g(x) = |4x + 3|

4) g(x) = 2x - 3

5) g(x) = 3x + 5

6) g(x) = ∣x - 4∣ − 3

7) g(x) = ∣x + 2 ∣ + 1

8) g(x) = -(1/2) (x) + 1

9) f(x) = 2x + 1

10) g(x) = (1/3) x + 3

11) f((1/2) x - 2) = ∣(1/2)x - 2|

12) g(x) = |x - 3|

13) a)  f(x) = 2x - 2

b) f(x) = 2x + 5

14) a) When reflection across x- axis, then put y = -y 

y = -|x + 3| - 1

b) When reflection across y- axis, then put x = -x

y = |x - 3| + 1