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Practice: Combining Function Transformations
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Practice Page

Directions: Read carefully.

1.
Given the parent function f (x) = x2.
Then g(x) = (x - 4)2 - 9 is the result of a shift of f (x)
Choose:
4 units left and 9 units down
4 units left and 9 units up
4 units right and 9 units down
4 units right and 9 units up

 

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2.
Considering the parent function to be f (x) = x2, the graph at the right can be represented by which equation?
Choose:
g(x) = f (x + 2) + 1
g(x) = f (x - 2) + 1
g(x) = f (x + 2) - 1
g(x) = f (x - 2) - 1

 

 

3.
Which transformation of f (x) moves the graph 3 units to the right and 1 unit up?

Choose:
g(x) = f (x + 3) - 1
g(x) = f (x + 3) + 1
g(x) = f (x - 3) - 1 g(x) = f (x - 3) + 1

 

 

4.
Given f (x) = | x | as the parent function. Which equation will move the graph 4 units to the left and 3 units up?
Choose:
g(x) = | x - 4 | + 3
g(x) = | x + 4 | + 3
g(x) = | x | - 4 + 3 g(x) = | x | + 4 + 3

 

 

5.
Compare the graph of h(x) = 4(x - 3)2 + 2 to the graph of  j (x) = x2.

Choose:
h(x) is wider than j (x), and its vertex is moved to the right 3 units and up 2 units
h(x) is wider than j (x), and its vertex is moved to the left 3 units and up 2 units
h(x) is narrower than j (x), and its vertex is moved to the left 3 units and up 2 units
h(x) is narrower than j (x), and its vertex is moved to the right 3 units and up 2 units

 

 

6.
The parent function for the graph at the right is . Which of the equations can represent the transformations shown at the right?

Choose:

 

 

7.
The parent function f (x) = | x | is transformed by two shifts:
vertical shift: k = -2
horizontal shift: k = 5
a) Which of the following equations represents these transformations?
Choose:
g(x) = | x - 2 | + 5
g(x) = | x + 2 | + 5
g(x) = | x + 5 | - 2
g(x) = | x - 5 | - 2

b) What are the coordinates of the vertex of g(x)?
Choose:
(5, -2)
(-5, 2)
(5, 2) (-5, -2)

 

 

8.
Function f (x) is shown at the right. Function g(x) is defined as
g(x) = f (x + 1) - 2. To what location will the point (-3,3) be moved under this transformation?

Choose:
(-4, 5)
(-2, 5)
(-4, 1)
(-2, 1)

 

 

9.
The parent function is y = | x |.
a) Which equation represents f (x)?
Choose:

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

b) Which equation represents g(x)?
Choose:
g(x) = | x + 4 |
g(x) = - | x | + 4
g(x) = | x | + 4 g(x) = - | x + 4 |
 
c) Which equation represents a transformation of f (x) to obtain g(x)?
Choose:
g(x) = - f (x) + 4
g(x) = f (x) + 3
g(x) = - (f (x) + 3) g(x) = - f (x) + 5

 

 

10.
Given function f (x) = 2x, and function g(x) is a transformation of f (x).
Which equation represents g(x)?

Choose:
g(x) = (2x + 1)
g(x) = (2x - 2)
g(x) = -(2x + 1)
g(x) = -2x + 1



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