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 | 8 units to the left | C | 8 units to the right | B | 8 units up | D | 8 units down |
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2.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 5 units down | C | 5 units right | B | 5 units left | D | 5 units up |
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3.
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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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4.
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Given the graph of f( x) shown below, what are the coordinates of
point A ¢ if the equation of the transformed function is  ? 
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5.
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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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6.
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Which radical equation can be solved using the graph shown below? 
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7.
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Which equation of a radical function would have the following domain and
range?  ; 
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8.
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Which graph represents an even-degree polynomial function with a
y-intercept of 9?
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9.
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If  is divided by  , then the restriction on x
is
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10.
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What is the remainder when  is divided by  ?
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11.
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If  is divided by  , what is the remainder? A | P(x – 4) | C | P(x +
4) | B | P(4) | D | P(–4) |
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12.
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A factor of  is A |  | C |  | B | x –
5 | D | x –
8 |
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13.
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Determine the value of k so that  is a factor of  . A | k = –1 | C | k = 14 | B | k = –14 | D | k = 1 |
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14.
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The graph that corresponds to the function  is
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15.
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Given the function  , what are the parameters of the transformed function
y =   and what is the effect of each parameter on the graph of
the original function? A | a =  , vertical stretch about the x-axis by a factor of
h = –8, horizontal translation 8 units right
k = 2, vertical
translation 2 units down | B | a =  , vertical stretch about
the x-axis by a factor of 
h = 2, horizontal translation 2 units
left
k = –8, vertical translation 8 units right | C | a =  ,
vertical stretch about the x-axis by a factor of 
h = 2, horizontal translation 2
units right
k = –8, vertical translation 8 units down | D | a =  ,
vertical stretch about the x-axis by a factor of 
h = 2, horizontal translation
2 units right
k = –8, vertical translation 8 units
down |
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Short Answer
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1.
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2.
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Jim states that the equations  and  have the same solution. Is
he correct? Justify your reasoning.
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3.
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Factor fully.
a) x3 + 6x2 +
11x + 6
b) 4x3 – 11x2 –
3x
c) x4 – 81
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4.
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Factor fully.
a) x2(x – 2)(x +
2) + 3x + 6
b) 16x4 – (x + 1)2
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5.
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Solve by graphing using technology. Round answers to one decimal place.
a) x3 – 7 > 0
b) 
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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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Show that x + a is a factor of the polynomial P(x) =
(x + a)4 + (x + c)4 – (a –
c)4.
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3.
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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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4.
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Create a cubic polynomial inequality for which x = 3 or 
is the solution. Explain your reasoning .
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5.
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Determine an equation for the polynomial function represented by the table of
values. x | y | –3 | –30 | –2 | –10 | –1 | –2 | 0 | 0 | 1 | 2 | 2 | 10 | 3 | 30 | | | | |
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