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 to the left | D | 5 units up |
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2.
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When b < 0, the function  has what relationship to the base
function  ? A | f(x) is stretched horizontally by a factor of 1/|b| and reflected in
the y-axis | B | f(x) is stretched vertically by a factor of |b| | C | f(x) is
stretched vertically by a factor of |b| and reflected in the x-axis | D | f(x) is
stretched horizontally by a factor of 1/|b| |
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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 | 9 units to the right and 5 units down | C | 5 units to the right and 9 units
up | B | 9 units to the right and 5 units up | D | 5 units to the right and 9 units
down |
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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 | 2 units to the right and 9 units down | C | 9 units to the left and 2 units
up | B | 9 units to the right and 2 units down | D | 2 units to the left and 9 units
up |
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5.
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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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6.
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What is the equation of the radical function shown in the graph below? 
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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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Which radical equation can be solved using the graph shown below? 
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10.
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What is the solution to the radical equation  ?
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Short Answer
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1.
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Jim states that the equations  and  have the same solution. Is
he correct? Justify your reasoning.
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2.
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Solve the equation  algebraically.
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Problem
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1.
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Two groups of students are conducting a lab to determine the relationship
between the period, p, in seconds, of a pendulum and the length, l, in metres, of the
string. The curves of best fit from the experiment are shown on the graph.  a)
When asked the type of function that could be used to model their findings, both groups argue that a
radical function can be used. Do you agree with each group? b) How do these graphs differ
from the graph of  ? c) Write a function to approximate the graph for
each group. d) What may have caused the differences in the data between the two groups?
Justify your answer in terms of transformations.
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2.
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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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