Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 9 units to the right | C | 9 units down | B | 9 units up | D | 9 units to the
left |
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2.
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When a > 0, the function  has what relationship to the base
function  ? A | f(x) is stretched vertically by a factor of |a| and reflected in the
x-axis | B | f(x) is stretched horizontally by a factor of 1/|a| | C | f(x) is
stretched vertically by a factor of |a| | D | f(x) is stretched horizontally by
a factor of 1/|a| and reflected in the y-axis |
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3.
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Which of the graphs shown below represents the base function  and the
stretched function g( x) =  x2?
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4.
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Compared to the graph of the base function  , the graph of the function
 is translated A | 4 units to the right and 8 units up | C | 8 units to the left and 4 units
down | B | 4 units to the left and 8 units down | D | 8 units to the right and 4 units
up |
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5.
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Which of the following angles, in degrees, is coterminal with, but not equal to,
  radians?
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6.
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A bottle is riding the waves at a beach. The bottle’s
up and down motion with the waves can be described using the formula  , where h is the
height, in metres, above the flat water surface and t is the time, in seconds. When is the
first time, to the nearest tenth of a second, that the height of the bottle will be 1.4
m?
A | 14.8 s | C | 0.9
s | B | 1.1 s | D | 1.5
s |
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7.
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What is the amplitude of the sinusoidal function  ? A |  | C | –5 | B | –8 | D | 7 |
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8.
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Which graph represents the sinusoidal function  ?
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9.
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Given the trigonometric function  , find the value of the
y-coordinate of the point with x-coordinate –1200°.
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10.
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What are the solutions for   = 0 in the interval  ? A | x = 90° and 270°  | C | x = 60° and 240° and 45° | B |     | D | x =
30° and 210°  |
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Use the following information to answer the questions.The height,
h, in centimetres, of a piston moving up and down in an engine cylinder can be modelled by the
function  , where t is the time, in seconds.
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11.
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What is the period?
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12.
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Which equation is a quotient identity?
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13.
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Which expression is equivalent to  ?
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14.
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Determine the exact value of  .
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15.
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Simplify  .
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16.
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Which expression is equivalent to  ?
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17.
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 can be rewritten as
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18.
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A radioactive sample with an initial mass of 1 mg has a half-life of 9 days.
What is the equation that models the exponential decay, A, for time, t, in 9-day
intervals?
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19.
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Solve for x. 
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20.
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The domain of the function  is
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21.
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Compared to the graph of the base function  , the graph of the function
 is translated A | 6 units to the right and 7 units up | C | 7 units to the right and 6 units
up | B | 7 units to the left and 6 units down | D | 6 units to the left and 7 units
down |
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22.
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Compared to the graph of the base function  , the graph of the
function  is A | translated down 10 units and left 6 units, horizontally stretched by a factor of  ,
reflected in the y-axis, vertically stretched by a factor of 3, and reflected in the
x-axis | C | translated down 10 units and left 6 units, horizontally stretched by a factor of  ,
not reflected in the y-axis, vertically stretched by a factor of 3, and not reflected in the
x-axis | B | translated down 10 units and right 6 units, horizontally stretched by a factor of
 , reflected in the y-axis, vertically stretched by a factor of 3, and not reflected in the
x-axis | D | translated up 10
units and left 6 units, horizontally stretched by a factor of  , not reflected in the
y-axis, vertically stretched by a factor of 3, and not reflected in the
x-axis |
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23.
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Which if the following is equivalent to the expression  ?
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24.
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Solve  . Round your answer to two decimal places.
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25.
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What is the equation for the horizontal asymptote of the graph of the function
shown? 
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26.
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Which function has a graph in the shape of a parabola?
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27.
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Solve the equation  . A | x =  | C | x =
–6 | B | x = –8 | D | x =  |
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28.
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Solve the equation  . A | x =  | C | x =  | B | x = 3 | D | x = 4 |
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29.
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What are the x-intercepts of the graph of  ?
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For the following question(s), assume that x is in radians, if
applicable.
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30.
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Given the functions  and  , what is the value of  ?
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31.
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If  and  , what are the restrictions on the domain
for the combined function  ?
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32.
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Solve for n in the expression  .
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33.
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A scout troop is arranged in a circle for an opening ceremony. If there are 9
scouts, in how many unique ways can they stand around the circle?
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34.
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After a sports, tournament every player shakes hands with every other player
once. If there are 36 handshakes in total, how many players are at the tournament?
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35.
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While at the dollar store, Peter finds 19 items at $1 each that he wants, but he
only has $3. The number of ways he could select which items to buy is
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Short Answer
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1.
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Find the exact value of  .
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2.
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Use a counterexample to show that  is not an identity.
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3.
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Verify graphically that  for  .
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4.
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Sketch the graph of the function  using transformations and
identify a) the vertical asymptotes (if any) b) the horizontal asymptotes (if
any) c) the domain and range d) the behaviour near any non-permissible
values e) the end behaviour 
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5.
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Problem
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1.
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Solve the equation  .
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2.
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a) Sketch the graph of the function  . Identify the key
features. b) Identify the domain and range. c) Identify the equation of the
vertical asymptote. 
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3.
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Find the difference in pH levels of a swimming pool with a hydronium ion
concentration of  mol/L and a swimming pool with a hydronium ion
concentration of  mol/L, to the nearest hundredth.
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4.
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Explain the steps used to solve the equation  .
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5.
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Write an equation for a rational function whose graph has all of the following
features: • vertical asymptote with equation x = 3 • horizontal asymptote
with equation y = 2 • hole at x = 1 • no x-intercepts
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