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Total questions: 21

Worksheet time: 1hrs 12mins

Name
Class
Date
1.
Given f(x) = (x-3)2 + 5.  What transformations took place from the original function f(x)?
a)
Left 3 and up 5
b)
Right 3 and down 5
c)
Left 3 and down 5
d)
Right 3 and up 5
2.
If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?
a)
-f(x)
b)
f(-x)
c)
f-1(x)
d)
f(2x)
3.
Identify the transformations. 
a)
horizontal shift to the left 2 and vertical stretch by a factor of 3
b)
horizontal shift to the right 2 and vertical stretch by a factor of 3
c)
horizontal shift to the right 2 and vertical shrink by a factor of 3
d)
horizontal shift to the left 2 and vertical shrink by a factor of 3
4.
Match the equation to its description.
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
5.
g(x)=-f(x)
Describe the transformation to f(x) that results in g(x).
a)
f(x) has been reflected over the x-axis.
b)
f(x) has been reflected over the y-axis.
6.
Identify the coordinates of the point (3 , -2), translated 5 units left and 6 units up.
a)
(2,-4)
b)
(-2,4)
c)
(8,4)
d)
(-2,-8)
7.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a translation shifting f(x) 4 units up
b)
a translation shifting f(x) 4 units down
c)
a translation shifting f(x) 4 units to the left
d)
a translation shifting f(x) 4 units to the right
8.
Which transformation will occur if f(x) = x2 is replaced with 2⋅f(x)?
a)
Vertical Compression by a factor of 2
b)
Vertical Stretch by a factor of 2
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
9.

A student graphed f(x) = x and g(x) = f(x) - 12. Which statement is true?

a)

The graph of f is shifted 12 units to the right to create the graph of g.

b)

The graph of f is shifted 12 units down to create the graph of g.

c)

The graph of f is shifted 12 units up to create the graph of g.

d)

The graph of f is shifted 12 units to the left to create the graph of g.

10.

A student graphed f(x) = x and g(x) = f(x - 15). Which statement is true?

a)

The graph of f is shifted 15 units to the right to create the graph of g.

b)

The graph of f is shifted 15 units down to create the graph of g.

c)

The graph of f is shifted 15 units up to create the graph of g.

d)

The graph of f is shifted 15 units to the left to create the graph of g.

11.
How did we transform from f(x) =x2 
to
g(x) = -3x2
a)
reflection in x-axis and vertical shift down
b)
reflection x-axis and vertical stretch
c)
horizontal stretch
d)
reflection x-axis and vertical compression
12.
If the blue graph is
f(x) = x2 
then the red must be...
a)
g(x) = x2 - 5
b)
g(x) = x2 + 5
c)
g(x) = (x - 5)2
d)
g(x) = (x + 5)2
13.

How did the equation shift from the parent function?

y = f(x) + c

a)

Shifted up "c" units

b)

Shifted down "c" units

c)

Stretches vertically

d)

Shifted right "c" units

14.

Which transformation on

f(x) = x

is g(x) = -f(x)

a)

Reflection across the y-axis

b)

The slope will be less steep

c)

The graph will be wider

d)

Reflection across the x-axis.

15.
Compare the function y = 0.3x2 to the parent function y = x2
a)
Wider
b)
Narrower
16.
Compare the function y = 5x2 to the parent function y = x2
a)
Wider
b)
Narrower
17.
Which transformation will occur if f(x) = x is replaced with f(x) + 2?
a)
Translation left 2 units
b)
Translation right 2 units
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
18.

How did the equation shift from the parent function? y = f(x - 4)

a)

Shift right by 4

b)

Shift left by 4

c)

Horizontal Stretch by 4

d)

Vertical Stretch by 4

e)

Shift down by 4

19.

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

a)

f(-2x - 4)

b)

f(-1/2x) - 4

c)

-f(2x) - 4

d)

-f(1/2x) - 4

20.
Describe the transformation of y = (x - 4)2
a)
Shift UP
b)
Shift DOWN
c)
Shift LEFT
d)
Shift RIGHT
21.
What transformations has the function undergone?
a)
reflect over y, vertical compress by 2, right 5, up 1
b)
reflect over x, horizontal compression by 2, left 5, up 1
c)
reflect over x, vertical stretch by 2, right 5, up 1
d)
reflect over y, horizontal stretch by -2, right 5, up 1

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