Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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In the following graph, which transformations must be applied to the blue curve
to obtain the red curve?  A | a reflection in the x-axis, a vertical translation of 4 units up, and a
horizontal translation of 3 units to the right | B | a reflection in the x-axis, a vertical
translation of 3 units up, and a horizontal translation of 4 units to the right | C | a reflection in the
x-axis, a vertical translation of 3 units down, and a horizontal translation of 4 units to the
right | D | a reflection in the x-axis, a vertical translation of 4 units up, and a
horizontal translation of 3 units to the left |
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2.
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In the graph shown, which transformations must be applied to the blue curve to
obtain the red curve?  A | a reflection in the x-axis and a translation of 5 units
down | B | a reflection in the y-axis and a translation of 5 units up | C | a reflection in the
x-axis and a translation of 5 units up | D | a reflection in the y-axis and a
translation of 5 units down |
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3.
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Which of the following graphs represents the graph of the function 
transformed to  ?
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4.
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Which of the following functions is the correct inverse for the function  ,
{ x | x ³ 0, x Î R}?
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5.
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Which of the following relations is the correct inverse for the function  ?
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6.
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Which graph represents the inverse of the graph shown? 
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7.
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The equation of the inverse of  is
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8.
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The two functions in the graph shown are reflections of each other. Select the
type of reflection(s).  A | a reflection in the y-axis | C | a reflection in the line y =
x | B | a reflection in the x-axis and the y-axis | D | a reflection in the
x-axis |
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9.
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Which is the graph of the square root of the function  ?
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10.
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Which of the following functions is the correct inverse for the function  ,
{ x | x ³ 0, x Î
R}?
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11.
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Which graph represents the square root of the graph shown? 
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12.
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If  is divided by  to give a quotient of  and a
remainder of –952, then which of the following is true?
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13.
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For a polynomial P( x), if  = 0, then which of
the following must be a factor of P( x)?
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14.
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Which of the following is the fully factored form of  ?
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15.
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Which of the following is not an asymptote of the function  ?
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Use the following information to answer the questions.The height,
h, in metres, above the ground of a car as a Ferris wheel rotates can be modelled by the
function  , where t is the time, in seconds.
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16.
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What is the radius of the Ferris wheel?
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17.
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How long does it take for the wheel to revolve once?
A |  s | C | 160 s | B | 80
s | D | 
s |
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18.
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What is the minimum height of a car?
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19.
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What is the maximum height of a car?
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20.
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Which of the following sets is the set of reciprocal trigonometric
ratios?
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21.
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Which choice best describes the function  ? A | both increasing and decreasing | C | increasing | B | decreasing | D | neither increasing nor decreasing |
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22.
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Which set of properties is correct for the function  ?
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23.
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The equation  can also be written as
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24.
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Which function is represented by the following graph? 
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25.
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Which graph represents the function  ?
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26.
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Which equation can be used to model the given information, where the population
has been rounded to the nearest whole number? Year (x) | Population
(y) | 0 | 100 | 1 | 104 | 2 | 108 | 3 | 112 | 4 | 117 | 5 | 122 | | |
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27.
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Solve for x.
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28.
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Which graph represents the inverse of  ?
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29.
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What is true about the behaviour of the function  as    (right to left)? A |  -¥ | C |  | B |  +¥ | D | f(x) is
undefined |
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30.
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Which of the following functions has a slant asymptote when graphed?
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31.
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Which function has vertical asymptotes with equations  and 
 ?
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32.
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Which graph represents  ?
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For the following question(s), assume that x is in radians, if
applicable.
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33.
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Given the functions  and  , the graph of the combined function 
most likely resembles
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34.
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Given the functions  and  , a graph of the combined function 
most likely resembles
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35.
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An equation for the graph shown is most likely 
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Short Answer
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1.
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The water level at an ocean inlet has a depth, d, in metres, that varies
with the time, t, in hours after midnight, according to the equation  . What is the
water depth at 2:30 a.m., to the nearest hundredth of a metre?
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2.
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For the function  , a) describe the transformations of the function
when compared to the function  b) sketch the graph of the given function and
 on the same set of axes c) state the domain, the range, and the equation of the
asymptote
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3.
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Sketch the graph of the function  .
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4.
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A certain type of exponential growth can be described by the equation  ,
where  is the initial amount; k is the doubling time, in years; and N is the
amount after time, t, in years, has passed. Suppose that the population of a small town
doubles every 25 years. How long does it take to triple, to the nearest tenth of a year?
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5.
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Show that  .
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Problem
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1.
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Solve  algebraically. Display your result on a number
line.
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2.
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In DABC, c = 11 cm, b = 7 cm, and ÐB = 38°.
a) Sketch possible diagrams for this
situation.
b) Determine the measure, to the nearest degree, of ÐC in each diagram.
c) Find the measure of ÐA in each diagram.
d) Calculate the length of BC in each
diagram.
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3.
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When a pendulum that is 0.5 m long swings back and forth, its angular
displacement, q, in radians, from rest position is given by  ,
where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum
displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at
t = 0.)
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4.
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Ingrid is docking a motorboat. She turns off the power and lets the boat coast
toward the dock. The distance, d, in metres, between the boat and the dock as a function of
time, t, in seconds, is given by  . a) What is the average velocity of the boat
during the time interval from when Ingrid turns the boat off to when it meets the dock? b)
Determine the velocity of the boat when Ingrid turns off the power, to one decimal place. c)
Determine the velocity of the boat when it meets the dock, to one decimal place. d)
Sketch the graph of the function. On the same set of axes, sketch the graph of the speed of
the boat in relation to the time.
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5.
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a) Use the asymptotes and intercepts to make a quick sketch of the
function  and its reciprocal  on the same set of axes. b) Describe the
symmetry in the graphs in part a). c) Determine the equation of the mirror line in your
graph from part a). d) Determine intervals where f is positive and where f is
negative. Determine intervals where g is positive and where g is negative.
How do the two sets of intervals compare to each other? e) Does the pattern from part d)
occur for all pairs of functions  and  ,  ? Explain why or why
not.
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