 Transformations of Functions Terms of Use    Contact Person: Donna Roberts  Directions: Read carefully. Choose the best answer.

1.
Given f (x) shown at the right.
Which graph choice depicts -f (x)?
Choose:     2.
The minimum point on the graph of the function y = f (x) is (-2,-4). What is the minimum point on the graph of the function y = f (x) + 7?

Choose:

 (-2, -11) (5, 3) (-2,3) (-5,-11) 3.
If the graph of the function y = 2x is reflected over the x-axis, the equation of the reflection is ___________.

Choose:
 y = 2-x y = x2 y = -(2x) y = -x2 4.
Function f (x) is shown in the table at the right. Which of the choices represents the value of h (3), given that h (x) = f (x) + 4?

Choose:
 7 -6 11 -10
 x f (x) 2 -12 3 -10 7 7 11 14 12 18

5.
Given g (x) shown at the right.
Which graph depicts g (x + 2)?
Choose:     6.
Function y = f (x) has been shifted 3 units to the right and 5 units down. Which of the following equations represents these changes?

Choose:
 y = f (x + 3) - 5 y = f (x - 3) + 5 y = f (x + 3) + 5 y = f (x - 3) - 5 7.
Which of the following statements describes the transformation indicated by: Choose:
 Function f was translated (shifted) horizontally 3 units to the left. Function f was translated (shifted) vertically 3 units down. Function f was translated (shifted) horizontally 3 units to the right. Function f was translated (shifted) vertically 3 up. -6 8.
Let x represent the length of the side of a square, and also the edge of a cube. The area of the square is represented by
f (x) = x2.
The surface area of the cube is represented by g(x) = 6x2.
Which statement describes
g(x) in terms of f (x)?
Choose:
 g(x) is a horizontal shrink of f (x). g(x) is a horizontal stretch of f (x). g(x) is a vertical shrink of f (x). g(x) is a vertical stretch of f (x). 9.
Given f (x) = 2x + 4.
Function g (x) = f (x) + 6.
a) What is the x-intercept of f (x)?
Choose:
 -2 2 4 6

b) What is the x-intercept of g (x)?
Choose:
 -10 -8 -5 -2

c)
What is the y-intercept of f (x)?
Choose:
 -2 2 4 6

d)
What is the y-intercept of g (x)?
Choose:
 24 10 8 6 10.
A parabolic function f (x) = x2 - 4.
Function g(x) is defined as g(x) = f (x) + 3.
What is the equation of g(x) in terms of x? Choose:
 g(x) = x2 - 7 g(x) = x2 + 1 g(x) = x2 + 7 g(x) = x2 - 1 11.
The shape of a roof is modeled by a transformation of the absolute value function, f (x) = | x |. The function is reflected in the x-axis, and translated 8 units up and 10 units to the right to create the roof model.
a) Which equation represents the model for the roof, r(x)?
Choose:
 r(x) = -|x - 10| + 8 r(x) = |x + 10| + 8 r(x) = |x + 8| - 10 r(x) = -|x - 8| + 10

b)
Which domain makes sense for r(x)?
Choose:
 0 < x < 10 2 < x < 18 2 < x < 22 0 < x < 16

c)
What is the bottom width of the model roof, if each unit represents one foot?
Choose:
 10 feet 18 feet 16 feet 20 feet 12.
Given: f (x) = x2 ; k = 2; c = 3.
Given transformation functions:
y1 = kf (x) + c and y2 = k[f (x) + c]

a)
Which of the two transformation functions is represented by the graph at the right?
Choose:
 y1 y2 b) Which transformation occurs first in function y1 ?
Choose:
 vertical stretch translation up

c)
Which transformation occurs first in function y2 ?
Choose:
 vertical stretch translation up

d)
The transformation functions y1 and y2 are congruent.
Choose:
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