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
x2
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
x2
c. f
1
( x)
1
x2
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
0
