PREC 12 Chapter ONE Review Date:

MULTIPLE CHOICE

1. A function )(xfy = is graphed. If )()( xfxg −= , then the graph of )(xgy = is the same as the graph of

a. )(xfy = reflected on the line xy = c. )(xfy = reflected on the x -axis

b. )(xfy = reflected on the y -axis d. the reciprocal of )(xfy =

2. 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

)(2)( xfxg = will have

a. The same domain and range as f c. a different domain but same range as f

b. 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 3xy = into the graph of ( )334 −=− xy , the point (3, 27) becomes the

point (6, y ). The value of y is

a. 31 b. 30 c. 23 d. 24

4. If y is replaced by 2

yin the equation )(xfy = , then the graph of )(xfy = will be stretched

a. Horizontally about the y -axis by a factor of 2

1 c. Vertically about the x -axis by a factor of

2

1

b. Horizontally about the y -axis by a factor of 2 d. Vertically about the x -axis by a factor of 2

5. Given the graph of )(xfy = below, which of the following graphs represents the transformed function

= xfy2

1?

c.

d.

6. The graphs of 3xy = was transformed to ( ) 43 3 +−= xy . 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. 3 units to the left and 4 down d. The point (x, y) has been translated to (x - 3, y - 4)

a.

b.

c.

7. Which of the following transformations of )(xfy = result in )(xgy = ?

8. Given the graph of )(xfy = , which of the following is the graph of 4)( −= xfy ?

a. c.

b. d.

9. The graph of )(xfy = , where 14)( ++= xxf , is reflected in the y-axis. This produced the same results as would

translating the graph of )(xfy = to the right by ______ units.

a. 4 units b. 1 unit c. 8 units d. 5 units

10. Given )(xfy = below, determine the range of 2)3()( +−= xfxg .

a.

b.

c.

d.

a.

b.

c.

d.

11. The function 3

2)(

2 +=

xxf and its reflection are shown below. An expression for this reflection is

12. How is the graph of 3)( −= xfy related to the graph of )(xfy = ?

a. )(xfy = has been translated 3 up c. )(xfy = has been translated 3 left

b. )(xfy = has been translated 3 down d. )(xfy = has been translated 3 right

13. Which equation represents the graph of )(xfy = after it is reflected in the line xy = ?

a. )( yfx = b. )( xfy −= c. )(xfy −= d. )(

1

xfy =

14. If the graph of the function xy = is horizontally expanded by a factor of 3 and then translated 2 units to the right,

determine the equation of this new function.

a. ( )23 −= xy b. ( )23

1 −= xy c. 23

1 −= xy d. 23 −= xy

15. If (4, 12) is a point on the graph )(xfy = , what must be a point on the graph of 3)2( +−= xfy ?

a. (4, -9) b. (4, 15) c. (2, -9) d. (2, -15)

16. The graph of )(xfy = is shown below on the left. Which equation represents the graph shown on the right?

17. Which equation represents the graph of )(xfy = after it is reflected in the x- axis?

a. )( xfy −= b. )(xfy −= c. )(1 xfy −= d. )(xfy =

a.

b.

c.

d.

a.

b.

c.

d.

18. If 1

2)(

−=

x

xxf , determine the equation of )(1 xfy −= , the inverse of )(xf .

a. 1

2)(1

−=−

x

xxf b.

2)(1

−=−

x

xxf c.

21

)(1

−=−

xxf d.

x

xxf

21

)(1 −=−

19. The graph of )(xfy = is graphed below on the left. Determine the equation of the function on the right.

20. If the range of )(xfy = is 53 ≤≤− y , determine the range of )(xfy =

a. 53 ≤≤− y b. 30 ≤≤ y c. 50 ≤≤ y d. 53 ≤≤ y

21. If the point (4, -9) is on the graph of )(xfy = , which of the following points must be on the graph of ))1(2(3

1 −= xfy ?

a. (3, -3) b. (9, -3) c. (9, 27) d. (3, -27)

22. The graph of )(xfy −= is a reflection of the graph of )(xfy = in which line?

a. the y axis b. the x axis c. the line xy = d. the line xy −=

23. The point (6, 1) is on the graph of the function )(xfy = . Which point must be on the graph of the function

?9)62(3 −+−= xfy

a. (0, 12) b. (-6, 6) c. (6, 1) d. (0, -6)

24. If the graph 832 =+ yx is translated 5 units down, determine the equation of the transformed graph.

a. 332 =+ yx b. 1332 =+ yx c. 8)5(32 =++ yx d. 8)5(32 =−+ yx

25. How is the graph of xy 46= related to the graph of

xy 6= ?

a. expanded vertically be a factor of 4 c. expanded horizontally by a factor of 4

b. compressed vertically be a factor of 4

1 d. compressed horizontally be a factor of

4

1

26. Determine the equation that will cause the graph of )(xfy = to expand vertically by a factor of 3 and reflect about the x

axis.

a. )(3 xfy −= b. )(3 xfy −= c. )(3

1xfy −= d. )(

31

xfy −=

a.

b.

c.

d.

27. If the graph of 922 =+ yx is horizontally compressed by a factor of 4

1, and then reflected in the y-axis, determine the

equation of the new graph.

a. 916

22

=+ yx

b. 916 22 =+ yx c. 916

22

=+− yx

d. 916 22 =+− yx

WRITTEN

28. The graph of )(xfy = is show below. Determine the equation for each of the transformed graphs.

```` a.

b.

29. Given )(xfy = below, sketch

30. Given )(xfy = below, sketch

a.

b.

c.

d.

a.

b.

a.

b.

c.

d.

e.