Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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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2.
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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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3.
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Which is the graph of the square root of the function  ?
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4.
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Which graph represents the square root of the function shown in the
graph? 
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5.
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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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6.
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Which graph represents the square root of the graph shown? 
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7.
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Which graph represents the square root of the graph shown? 
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8.
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Which graph shows the graphical solution to the radical equation  ?
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9.
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Which graph shows the graphical solution to the radical equation  ?
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10.
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If  is divided by  to give a quotient of  and a
remainder of –952, then which of the following is true?
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11.
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For a polynomial P( x), if  = 0, then which of the
following must be a factor of P( x)?
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12.
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Which of the following is the fully factored form of  ?
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13.
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Which of the following is the fully factored form of  ?
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14.
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Which of the following graphs of polynomial functions corresponds to a cubic
polynomial equation with roots 4, 1, and 3?
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15.
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Which of the following graphs of polynomial functions corresponds to a
polynomial equation with zeros –6 (multiplicity of 2) and –1 (multiplicity of 2)?
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Short Answer
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1.
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Create a graph of  for each base function given, using
transformations. a)  b) 
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2.
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3.
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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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4.
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a) Use long division to divide x3 +
3x2 – 7 by x + 2. Express the result in quotient form.
b)
Identify any restrictions on the variable.
c) Write the corresponding statement that can be
used to check the division.
d) Verify your answer.
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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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Consider the function  . a) Determine the square root
of the function. b) Graph the functions on the same set of axes. c) State the
domains and ranges of the graphs. d) Describe the relationship between the domain and range
of f( x) and the domain and range of g( x) .
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2.
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Factor 3x4 + 5x3 –
13x2 – x + 6 fully.
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3.
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Prove that x2 + 5x + 6 is a factor of
x4 + 5x3 + 2x2 – 20x –
24.
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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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Amit has designed a rectangular storage unit to hold large factory equipment.
His model has dimensions 1 m by 2 m by 4 m. By what amount should he increase each dimension to
produce an actual storage unit that is 9 times the volume of his model?
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