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 | 6 units down | C | 6 units up | B | 6 units right | D | 6 units left |
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2.
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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 reflected in the
y-axis | B | stretched by a factor of 8 and reflected in the y-axis | C | stretched by a factor
of 8 and not reflected | D | compressed by a factor of  and not
reflected |
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3.
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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| and reflected in the
x-axis | C | f(x) is stretched vertically by a factor of |b| | D | f(x) is
stretched horizontally by a factor of 1/|b| |
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4.
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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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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 are the coordinates of the invariant point(s) when the function  is
reflected in the x-axis? A | (0, 9) | C | (0, –3) | B | (9, –3) | D | (9, 0) |
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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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When solving the equation  , which values must be checked for
extraneous roots? A | 9 and 2 | C | 7 and –5 | B | 9 and –2 | D | –2 and 2 |
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Short Answer
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1.
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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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Graph the functions below, and then identify and compare their domains and
ranges.  and 
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