Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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 line y = x | C | a reflection in the
y-axis | B | a reflection in the x-axis and the y-axis | D | a reflection in the
x-axis |
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2.
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Which is the graph of the function  ?
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3.
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Which choice best describes the combination of transformations that must be
applied to the graph of  to obtain the graph of  ? A | a horizontal stretch by a factor of 2 and a horizontal translation of 2 units to the
left | B | a horizontal stretch by a factor of  and a horizontal translation of 4 units
to the right | C | a horizontal stretch by a factor of  and a horizontal translation of 2 units
to the right | D | a horizontal stretch by a factor of –2 and a horizontal translation of 2 units
to the right |
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4.
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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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5.
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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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6.
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When the function  is transformed to  , the graph looks
like
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7.
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Which of the following functions is the correct inverse for the function
f( x) =   ?
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8.
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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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9.
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In the following graph, what transformations must be applied to the blue curve
to obtain the red curve?  A | a reflection in the x-axis, a vertical translation 5 units up, and a
horizontal translation 3 units to the right | B | a reflection in the x-axis, a vertical
translation 5 units down, and a horizontal translation 3 units to the right | C | a reflection in the
x-axis, a vertical translation 3 units up, and a horizontal translation 5 units to the
left | D | a reflection in the x-axis, a vertical translation 3 units up, and a
horizontal translation 5 units to the right |
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10.
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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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11.
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Which is the graph of the square root of the function  ?
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12.
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Which graph represents the square root of the function shown in the
graph? 
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13.
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Which graph shows the graphical solution to the radical equation  ?
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14.
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Which graph shows the graphical solution to the radical equation  ?
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15.
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Which of the following is the fully factored form of  ?
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16.
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The graph of  can be obtained by translating the graph of  A |  units to the right | C |  units to the
right | B |  units to the right | D |  units to the
right |
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17.
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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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18.
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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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19.
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What is the minimum 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 expression is equivalent to  ?
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22.
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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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23.
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Which set of properties is correct for the function  ?
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24.
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For the exponential function  , which of the following statements is
not true? A | The graph of the function is increasing. | B | The graph of the
function is decreasing. | C | The domain is the set of real
numbers. | D | The range is the set of real numbers greater than
zero. |
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25.
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Which function results when the graph of  is translated 2 units
down?
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26.
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Which function is represented by the following graph? 
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27.
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Which function results when the graph of the function  is reflected
in the y-axis, compressed vertically by a factor of  , and shifted 2 units down?
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28.
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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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29.
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Solve for x, to one decimal place.  A | 1466.6 | C | 36 667.0 | B | 11.1 | D | 5.5 |
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30.
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Which graph represents the inverse of  ?
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31.
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Which of the following functions has a slant asymptote when graphed?
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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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Given the functions  and  , which of the following is most likely
the graph of  ?
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Short Answer
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1.
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Given that  and that x lies in the first quadrant, determine
the exact measure of angle x.
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2.
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A Ferris wheel of diameter 18.5 m rotates at a rate of 0.2 rad/s. If passengers
board the lowest car at a height of 3 m above the ground, determine a sinusoidal function that models
the height, h, in metres, of the car relative to the ground as a function of the time,
t, in seconds.
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3.
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Given the functions  and  , determine a simplified equation for
 .
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4.
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Joe wants to travel from his home to school. The school is 6 blocks east and 6
blocks north. How many routes can Joe take from his house to school if he only moves east and
north. 
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5.
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A math teacher is preparing a quiz for all of the students in grade 12. She
wants to give each student the same questions, but have each student’s questions appear in a
different order. If there are 128 students in the grade 12 class, what is the least number of
questions the quiz must contain so everyone gets a test with the questions in a different
order.
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Problem
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1.
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The table shows the fraction of the Moon that can be seen at midnight from
Simone’s town. Day 1 represents January 1. Day | 1 | 2 | 3 | 4 | 5 | 6 | 10 | 14 | 19 | 21 | Fraction
Visible | 0.25 | 0.17 | 0.12 | 0.06 | 0.02 | 0.00 | 0.10 | 0.56 | 0.98 | 1.00 | | | | | | | | | | | |
| Day | 24 | 30 | 35 | 41 | 45 | 51 | 56 | 60 | 65 | 66 | Fraction
Visible | 0.78 | 0.33 | 0.02 | 0.15 | 0.65 | 1.00 | 0.78 | 0.30 | 0.01 | 0.00 | | | | | | | | | | | |
a) What is the period of the sine function that could be used to
model the data? b) What is the amplitude of the function? c) What is the phase
shift of the function? d) What is the vertical shift? e) Use your answers to
parts a) to d) to write an equation for the function. f) Use your function to determine the
fraction of the moon visible to Simone on day i) 100 ii) 150 iii)
200
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2.
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The flapping of a bird’s wing can be modelled by the function  ,
where y represents the distance the tip of the wing travels, in centimetres, and t
represents the time, in seconds. a) Determine the period of the motion of the
wing. b) Determine the amplitude, the minimum value, and the maximum value. c)
What are the first times after t = 0 that the tip of the wing reaches the minimum and maximum
values? d) Determine the position of the wing tip at i) 
s ii)  s iii)  s
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3.
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a) The graph of a function of the form  is shown. Determine the
key features: i) domain and
range ii) intercepts
iii) equations of any asymptotes  b) State a
possible equation for this function.
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4.
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5.
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The revenue function for a company selling n key chains is given
by  , and the total cost function is given by  . Determine the simplified equation for
 , the profit function for the company.
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