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 | 2 units up | C | 2 units to the left | B | 2 units to the right | D | 2 units down |
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2.
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Which of the graphs shown below represents the base function  (in black) and
the stretched function g( x) =   (in red)?
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3.
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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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4.
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Given the function  , which of the following is a restriction on the inverse
function,  ?
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5.
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Which of the graphs shown below represents the base function  (in black) and
the stretched function g( x) =  (in red)?
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6.
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What are the coordinates of the invariant point(s) when the function  is
reflected in the y-axis? A | (9, –3) | C | (0, –3) | B | (–3, 0) and (9, 0) | D | (0, 9) |
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7.
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Which graph shows the solution to the radical equation  ?
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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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What is the solution to the radical equation  ?
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10.
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What is the solution to the radical equation  ?
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11.
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Which graph represents an odd-degree polynomial function with two
x-intercepts?
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12.
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Which graph represents an even-degree polynomial function with a
y-intercept of 9?
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13.
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A factor of  is A |  | C |  | B | x –
5 | D | x –
8 |
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14.
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Which set of values for x should be tested to determine the possible
zeros of  ? A | ±5, ±7, and ±35 | C | 1, 5, 7, 12, and
35 | B | ±1, ±5, ±7, and ±35 | D | 1, 5, 7, and 35 |
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15.
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The graph that corresponds to the function  is
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Short Answer
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1.
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Determine the equation of each radical function, which has been transformed from
 by the given translations. a) vertical stretch by a factor of 5, then a
horizontal translation of 6 units right b) horizontal stretch by a factor of  ,
then a vertical translation of 4 units down c) horizontal
reflection in the y-axis, then a vertical translation of 9 units up and horizontal translation
of 2 units right d) horizontal stretch by a factor of  , vertical reflection in
the x-axis, and vertical stretch by a factor of 
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2.
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3.
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Solve the equation  graphically.
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4.
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A student designs a special container as part of an egg drop experiment. She
believes that the container can withstand a fall as long as the speed of the container does not
exceed 80 ft/s. She uses the equation  to model the velocity, v, in feet per second, as a
function of constant acceleration, a, in feet per second squared and the drop distance,
d, in feet. Assuming the student’s specifications are correct, will the egg break if the
student drops the egg from shoulder height (5 ft) off a building 80 ft high? What is the maximum
height the egg can be dropped from? (Note: The acceleration due to gravity is 32
ft/s 2.)
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5.
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Solve.
a) 3x3 + 2x2 –
8x + 3 = 0
b) 2x3 + x2 – 10x
– 5 = 0
c) 5x4 = 7x2 – 2
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Problem
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1.
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The manufacturer of a new Global Positioning Satellite (GPS) system wants to
predict the consumer interest in its new device. The company uses the function  to model the
number, I, in thousands, of pre-orders for the GPS as a function of the number, w, of
weeks before the GPS release date. a) What are the domain and range and what do they mean
in this situation? b) Identify the transformations represented by the function compared to
 . c) Graph the function and explain what the shape of the graph indicates about
the situation. d) Determine the number of pre-orders the manufacturer can expect to have 10
weeks before the release date.
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2.
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For  and  , do the following. a) Graph
f( x) and g( x) on the same set of axes. b) Determine the domain
and range of each function. c) Explain which transformations would need to be applied to
the graph of f( x) to obtain the graph of g( x).
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3.
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Sun-Eui, a graduate student, is using the function  to model the number of
flowers a new hybrid bee can pollinate. For the function, N represents the number, in
thousands, of flowers pollinated and t represents the time, in days. a) If there are
10 000 flowers, how long will it take to pollinate all of the flowers? b) Sun-Eui believes
that the second generation of bees can reduce the time to pollinate the flowers by half by changing
the function to  . Is she correct? Justify your reasoning. c)
Should Sun-Eui continue with the project?
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4.
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The height, h, in metres, of a weather balloon above the ground after
t seconds can be modelled by the function h( t) = –2 t3 +
3 t2 + 149 t + 410, for  . When is the balloon exactly 980 m above
the ground?
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5.
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Maria is designing a series of stationery trays for holding paper and envelopes.
Each tray starts as a rectangular sheet of metal from which identical squares are cut from the four
corners. The resulting rectangular flaps are then folded up and welded to produce an open-topped
rectangular tray. What size square should Maria cut from a rectangular sheet of metal 15 cm by 25 cm
in order to produce a tray with a volume of 476 cm3? Round to the nearest hundredth of a
centimetre, if necesary.
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