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 | 5 units to the right | C | 5 units down | B | 5 units up | D | 5 units to the
left |
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2.
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What is the equation of the transformed function, g( x), after the
transformations are applied to the graph of the base function  , shown in blue, to
obtain the graph of g( x), shown in red? 
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3.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 9 units to the left and 4 units down | C | 9 units to the right and 4 units
up | B | 4 units to the left and 9 units down | D | 4 units to the right and 9 units
up |
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4.
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Compared to the graph of the base function  , the graph of the
function  is A | compressed by a factor of  and not reflected | B | stretched by a factor
of 5 and reflected in the y-axis | C | compressed by a factor of  and reflected
in the y-axis | D | stretched by a factor of 5 and not reflected |
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5.
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Given the function  with a domain of  and a range of  ,
which of the following best describes the vertical and horizontal translations with respect to the
graph of  ? A | 5 units to the left and 8 units up | C | 8 units to the left and 5 units
up | B | 8 units to the left and 5 units down | D | 5 units to the left and 8 units
down |
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6.
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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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7.
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What is the equation of the transformed function, g( x), after the
transformations are applied to the graph of the base function  , shown in blue, to
obtain the graph of g( x), shown in red? 
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8.
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Which graph shows the solution to the radical equation  ?
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9.
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When solving the equation  , which values must be checked for
extraneous roots? A | –4 and 7 | C | 8 and 6 | B | 7 and –7 | D | –4 and
–7 |
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10.
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Which equation of a radical function would have the following domain and
range?  ; 
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11.
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  radians is equal to how many degrees?
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12.
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Giai got an answer of 3.86 when she was calculating the value of a trigonometric
function. Assuming Giai did her calculation correctly, which of the following was she
calculating?
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13.
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Which function, where x is in radians, is represented by the graph shown
below? 
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14.
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The range (in radians) of the graph of  is
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15.
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The amplitude and period (in degrees) of  are A | amplitude = 
period =  | C | amplitude = 
period =
 | B | amplitude = 2
period =  | D | amplitude = –2
period =  |
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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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16.
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What is the period?
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17.
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Which equation is a reciprocal identity?
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18.
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Determine the exact value of  .
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19.
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Simplify  .
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20.
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 can be rewritten as
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21.
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A rumour is being spread in a community that the mayor is going to retire before
the next election. Initially, 6 people were told the rumour and each of these people told 6 others
the following day. Each of the 6 people told by the initial people told 6 others the day after they
were told. If this process keeps up, how many people will be told the rumour on the eighth
day?
A | 1 679 616 people | C | 10 077 696 people | B | 279 936 people | D | 48 people |
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22.
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Another way of writing  is
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23.
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Evaluate  .
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24.
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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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25.
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What is the equation for the asymptote of the function  ? A | x = 2 | C | x = –5 | B | x = –3 | D | x =
–2 |
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26.
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Which of the following is equivalent to the expression  ?
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27.
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If  ,  , and  , an algebraic expression
in terms of s, v, and z for  is A | v - 2s + 2z | C | v - 2(s - z) | B | v - 2(s + z) | D | v - 2s
+ z |
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28.
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Solve  . A | x = 6 | C | x =  | B | x =  | D | x =
729 |
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29.
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What are the x-intercepts of the graph of  ?
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30.
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Given the functions  and  , determine the equation for the combined
function  .
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For the following question(s), assume that x is in radians, if
applicable.
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31.
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Given the functions  and  , what is the range of the composite
function  ?
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32.
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Given the functions  and  , what is the simplified form of  ?
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33.
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Evaluate  . A | 32 432 400 | C | 6435 | B | 163 459 296 000 | D | 259 459 200 |
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34.
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Solve for the variable:  = 252 A | 15 | C | 6 | B |  | D |  |
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35.
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Prom’s friend gives him a row of Pascal’s triangle and asks which
row it comes from. Prom adds the numbers and obtains a sum of 65 536. Which row do the numbers come
from?
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Short Answer
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1.
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a) Sketch the graph of each function  , and then sketch the
graph of  . i)  ii)  iii)  b)
State the domain and range of each f( x) and g( x).
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2.
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Solve by graphing using technology. Round the root(s) to one decimal place.
a) x4 + x3 + x2 + x =
1
b) 0.1x4 = x3 + x2
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3.
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Determine the exact value of  .
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4.
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Solve the equation  . Leave your answer in exact form.
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5.
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Consider the function  . a) Determine the key
features of the function: i) domain and
range ii) intercepts
iii) equations of any asymptotes b) Sketch the graph of the function. 
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Problem
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1.
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Two wires are connected to a tower at the same point on the tower. Wire #1 makes
an angle of 45° with the ground and wire #2 makes an angle of 60° with the
ground.
a) Represent this situation with a diagram.
b) Which wire is longer?
Explain.
c) If the point where the two wires connect to the tower is 35 m above the ground,
determine exact expressions for the lengths of the two wires.
d) Determine the length of
each wire, to the nearest tenth of a metre.
e) How do your answers to parts b) and d)
compare?
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2.
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Cobalt-60, which has a half-life of 5.3 years, is used in medical radiology. A
sample of 60 mg of the material is present today.
a) Write an equation to relate the amount
of cobalt-60 remaining and the number of half-life periods.
b) What amount will be present
in 10.6 years?
c) How many years will it take for the amount of cobalt-60 to decay to 12.5%
of its initial amount?
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3.
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The pressure exerted on the floor by the heel of someone’s shoe is
inversely proportional to the square of the width of the heel of the shoe. When Megumi wears
2-cm-wide heels, she exerts a pressure of 400 kPa.
a) Determine a function to represent
the pressure, p, exerted by Megumi if she wears heels of width w.
b) Sketch
the graph of this function.
c) If she wears spike heels with a width of 0.5 cm, what
pressure does she exert?
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4.
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The revenue function for a school group selling n bookmarks is
given by  , and the total cost function is given by  . Determine the number of bookmarks that
need to be sold for the school group to break even.
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5.
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Expand and simplify:  .
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