WRITING EQUATIONS OF TRANSFOMRED FUNCTIONS WORKSHEET

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

Problem 1 :

f(x) = 3x, translation 5 units up.

Solution

Problem 2 :

f(x) = |x| - 3, translation 4 units to the right.

Solution

Problem 3 :

f(x) = -|x + 2| - 1 , reflection in the x-axis.

Solution

Problem 4 :

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

Solution

Problem 5 :

f(x) = x -  5, translation 4 units to the left.

Solution

Problem 6 :

f(x) = x + 2, translation 2 units to the left.

Solution

Problem 7 :

f(x) = |4x+3| + 2, translation 2 units down.

Solution

Problem 8 :

f(x) = 2x - 9, translation 2 units up.

Solution

Given the parent function and a description of the transformation, write the equation of the transformed function f(x) :

Problem 9 :

Square root function

Reflected in the x-axis

Translated 12 units down.

Solution

Problem 10 :

Absolute value function

Translated 12 units up

Translated 23 units left

Solution

Problem 11 :

Reciprocal function

Expanded vertically by the factor of 4

Reflected in the x-axis and translated 2 units up.

Solution

Problem 12 :

Write a rule for g described by the transformation of the graph of f. 

f(x) = x², vertical shrink by a factor of 1/2 and a reflection in the y-axis followed by a translation 2 units left.

Solution

Problem 13 :

Identify the parent function and describe the transformation :

a) f(x) = (x + 4)³

b) f(x) = -2|x - 4|

Solution

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 5 :

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

Solution

Problem 6 :

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

Solution

Problem 7 :

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

Solution

Problem 8 :

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

Solution

Problem 9 :

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

Solution

Problem 10 :

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

Solution

Problem 11 :

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

Solution

Problem 12 :

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

Solution

Problem 13 :

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 14 :

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

y = -|x + 3| - 1

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

y = |x - 3| + 1