Practice Page

Directions: Read carefully.

1.
Given the function f (x) = 3x.
If f (x) is increased by 5 units, the graph of the new function will be shifted 5 units _________.

Choose:
right
left
up
 down

 

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2.
The minimum point on the graph of f (x) is (-2,-6).
What is the minimum point on the graph of the function
f (x) - 4?
Choose:
(2,-6)
(-6,-6)
(-2,-10)
 (-2,-2)

 

 

3.
Given f (x) = -2x + 3. If g(x) = f (x) - 8, which choice represents the re-write for g(x)?

Choose:
g(x) = -2x + 11
g(x) = -10x + 3
g(x) = -2x - 5 g(x) = 6x + 3

 

 

4.
Given f (x) = 2x and g(x) = 2x - 4.
Which transformation of f (x) results in g(x)?

Choose:
(x, y) → (x, y - 4)
(x, y) → (x, y + 4)
(x, y) → (x - 4, y) (x, y) → (x + 4, y)

 

 

5.
Given f (x) = (x - 1)2 and g(x) = (x - 4)2.
When compared to f (x), the graph of g(x) is
Choose:
shifted 3 units to the right
shifted 3 units to the left
shifted 4 units to the right
shifted 4 units to the left

 

 

6.
Given f (x) = x2 - 2. If f (x) is shifted 5 units to the left to create function g(x), which choice will represent g(x)?

Choose:
g(x) = x2 - 7
g(x) = x2 + 3
g(x) = (x - 5)2 - 2 g(x) = (x + 5)2 - 2

 

 

7.
Regarding the graph at the right:
a) Which of the following equations represents the function f (x)?
 Choose:
f (x) = (x - 2)2
f (x) = x2 - 2
f (x) = (x + 2)2
f (x) = x2 + 2

b) If function g(x) = f (x) + k, what is the value of k?
Choose:
-2
2
3 -3
pP2

 

 

8.
The graph at the right is an offspring of the absolute value function. Which of the following equations represents f (x) as shown?

Choose:
f (x) = | x | - 2
f (x) = | x - 2 |
f (x) = | x | + 2
f (x) = | x + 2 |

 

 

9.
Function f (x) = x2 - 1 is horizontally shifted
by k = 2.
a) What is the axis of symmetry of the shifted function?
Choose:
x = -1
x = 2
x = - 2 x = 0

b) If the point (3, 8) lies on f (x), which point corresponds to this point on the shifted function?
Choose:
(1, 8)
(3, 6)
(5, 8) (3, 10)

 

 

 

10.
Given function f (x) = x3, and function g(x) = f (x + k).
a) What is the value of k?
Choose:
k = -2
k = 2
k = 3 k = -3

b) Which equation represents g(x)?
Choose:
g(x) = (x - 3)3
g(x) = (x + 3)3
g(x) = x3 - 2 g(x) = x3 + 3



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