Chapter 1 Transformations Review
PC 12
MULTIPLE CHOICE
1.
A function y  f (x) is graphed. If g ( x)   f ( x) , then the graph of y  g (x ) is the same as the graph of
a.
b.
2.
c. y  f (x ) reflected on the x -axis
d. the reciprocal of y  f (x )
The graph of a function f is a parabola opening upward, with its vertex on x -axis. The graph of a new function
g , where g ( x )  2 f ( x ) will have
a.
b.
3.
y  f (x) reflected on the line y  x
y  f (x) reflected on the y -axis
The same domain and range as f
c. a different domain but same range as f
The same domain but a different range than f d. a different domain and a different range than f
3
As a result of the transformation of the graph of y  x 3 into the graph of y  4   x  3 , the point (3, 27)
becomes the point (6, y ). The value of y is
a.
31
b. 30
c. 23
d. 24
y
in the equation y  f (x ) , then the graph of y  f (x ) will be stretched
2
1
1
a. Horizontally about the y -axis by a factor of
c. Vertically about the x -axis by a factor of
2
2
b. Horizontally about the y -axis by a factor of 2 d. Vertically about the x -axis by a factor of 2
4.
If y is replaced by
5.
Given the graph of y  f (x ) below, which of the following graphs represents the transformed function
1 
y  f  x ?
2 
6.
a.
c.
b.
d.
3
The graphs of y  x 3 was transformed to y   x  3  4 . Which of the following statements describes the
transformation?
a.
Translation 4 units to the right and 3 up
c. The point (x, y) has been translated to (x + 3, y +4)
b.
7.
8.
3 units to the left and 4 down
d. The point (x, y) has been translated to (x - 3, y 4)
Which of the following transformations of y  f (x ) result in y  g (x ) ?
1
f ( x)
a.
g( x) 
b.
g ( x)  f ( x)
c.
g( x) 
1
f ( x)
d.
g( x) 
1
f ( x)
Given the graph of y  f (x ) , which of the following is the graph of y  f ( x )  4 ?
a.
c.
b.
9.
d.
The graph of y  f (x ) , where f ( x )  x  4  1 , is reflected in the y-axis. This produced the same results as
would translating the graph of y  f (x ) to the right by ______ units.
a.
4 units b. 1 unit
c. 8 units
d. 5 units
10. Given y  f (x ) below, determine the range of g ( x )  f ( x  3)  2 .
a.
b.
c.
d.
g ( x)  11
g ( x )  9
g ( x )  8
g ( x)  0
11. The function f ( x ) 
2
x 3
2
and its reflection are shown below. An expression for this reflection is
a.
b.
c.
d.
x y
x  f ( y)
y  f ( x)
y   f (x )
12. How is the graph of y  f ( x )  3 related to the graph of y  f (x ) ?
a.
b.
y  f (x) has been translated 3 up
y  f (x) has been translated 3 down
c. y  f (x ) has been translated 3 left
d. y  f (x ) has been translated 3 right
13. Which equation represents the graph of y  f (x ) after it is reflected in the line y  x ?
a.
x  f ( y)
b. y  f (  x )
c. y   f (x )
d. y 
1
f ( x)
14. If the graph of the function y  x is horizontally expanded by a factor of 3 and then translated 2 units to the
right, determine the equation of this new function.
a.
y  3 x  2 
b. y 
1
x  2
3
c. y 
1
x2
3
d. y  3x  2
15. If (4, 12) is a point on the graph y  f (x ) , what must be a point on the graph of y   f (2 x )  3 ?
a.
(4, -9)
b. (4, 15)
c. (2, -9)
d. (2, -15)
16. The graph of y  f (x ) is shown below on the left. Which equation represents the graph shown on the right?
a.
b.
c.
d.
y  f ( ( x  8))
y  f ( ( x  8))
y   f ( x  8)
y   f ( x  8)
17. Which equation represents the graph of y  f (x ) after it is reflected in the x- axis?
a.
y  f ( x)
b. y   f (x )
c. y  f 1 ( x )
d. y  f (x )
18. If f ( x ) 
a.
2x
, determine the equation of y  f 1 ( x ) , the inverse of f (x ) .
x 1
f 1 ( x ) 
2x
x 1
b. f
1
( x) 
x
x2
c. f
1
( x) 
1
x2
d. f
1
( x) 
x 1
2x
19. The graph of y  f (x ) is graphed below on the left. Determine the equation of the function on the right.
1 
y  f  x
2 
y  f (2 x )
1
y  f ( x)
2
y  2 f ( x)
a.
b.
c.
d.
20. If the range of y  f (x ) is  3  y  5 , determine the range of y  f (x )
a.
3 y  5
b. 0  y  3
c. 0  y  5
d. 3  y  5
21. If the point (4, -9) is on the graph of y  f (x ) , which of the following points must be on the graph of
y
a.
1
f (2( x  1)) ?
3
(3, -3)
b. (9, -3)
c. (9, 27)
d. (3, -27)
22. The graph of y   f (x ) is a reflection of the graph of y  f (x ) in which line?
a.
the y axis
c. the line y  x
b. the x axis
d. the line y   x
23. The point (6, 1) is on the graph of the function y  f (x ) . Which point must be on the graph of the function
y  3 f ( 2 x  6)  9 ?
a.
(0, 12)
b. (-6, 6)
c. (6, 1)
d. (0, -6)
24. If the graph 2 x  3 y  8 is translated 5 units down, determine the equation of the transformed graph.
a.
2x  3y  3
b. 2 x  3 y  13
c. 2 x  3( y  5)  8
d. 2 x  3( y  5)  8
25. How is the graph of y  6 4 x related to the graph of y  6 x ?
a.
expanded vertically by a factor of 4
b.
1
compressed vertically by a factor of
4
c. expanded horizontally by a factor of 4
d. compressed horizontally by a factor of
1
4
26. Determine the equation that will cause the graph of y  f (x ) to expand vertically by a factor of 3 and reflect
about the x axis.
a.
y  3 f ( x)
b. y  3 f (  x )
c. y  
1
f ( x)
3
d. y 
1
f ( x)
3
1
27. If the graph of x 2  y 2  9 is horizontally compressed by a factor of , and then reflected in the y-axis,
4
determine the equation of the new graph.
a.
ANSWERS
1. C
2. A
3. A
4. D
5. D
6. C
7. B
8. A
9. C
10. B
11. B
12. B
13. A
14. B
15. C
16. B
17. B
18. B
19. A
20. C
21. A
22. B
23. D
24. C
25. D
26. A
27. B
x2
 y2  9
16
b. 16 x 2  y 2  9
c. 
x2
 y2  9
16
d.  16 x 2  y 2  9