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, which transformations must be applied to the blue curve
to obtain the red curve?  A | a reflection in the x-axis, a vertical translation of 4 units up, and a
horizontal translation of 3 units to the right | B | a reflection in the x-axis, a vertical
translation of 3 units up, and a horizontal translation of 4 units to the right | C | a reflection in the
x-axis, a vertical translation of 3 units down, and a horizontal translation of 4 units to the
right | D | a reflection in the x-axis, a vertical translation of 4 units up, and a
horizontal translation of 3 units to the left |
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2.
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In the graph shown, which transformations must be applied to the blue curve to
obtain the red curve?  A | a reflection in the x-axis and a translation of 5 units
down | B | a reflection in the y-axis and a translation of 5 units up | C | a reflection in the
x-axis and a translation of 5 units up | D | a reflection in the y-axis and a
translation of 5 units down |
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3.
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Which graph represents the inverse of the graph shown? 
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4.
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Which graph represents the inverse of the function shown? 
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5.
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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 up | D | 5 units to the
left |
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6.
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Given the graph of f( x) shown below, what are the coordinates of
point A if the transformed graph is represented by  ? 
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7.
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The function  represents a transformation that can best be described as
A | a reflection in the x-axis | C | a reflection in the
y-axis | B | a reflection in the x-axis and the y-axis | D | a reflection in the line y =
x |
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8.
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When b > 0, the function  has what relationship to the base
function  ? A | f(x) is stretched vertically by a factor of |b| and reflected in the
x-axis | B | f(x) is stretched vertically by a factor of |b| | C | f(x) is
stretched horizontally by a factor of 1/|b| and reflected in the y-axis | D | f(x) is
stretched horizontally by a factor of 1/|b| |
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9.
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What are the coordinates of the invariant point(s) when the function  is
reflected in the y-axis? A | (2, –2) | C | (0, –2) | B | (–2, 0) and (2, 0) | D | (0, 2) |
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10.
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When the value of a is less than –1, the function 
has what relationship to the base function  ? A | f(x) is compressed vertically | B | f(x) is
reflected and compressed vertically | C | f(x) is stretched
vertically | D | f(x) is reflected and stretched
vertically |
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Short Answer
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1.
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Given the graph of a function, sketch the resulting graph after the specified
transformation. a) reflection in the x-axis  b)
reflection in the y-axis  c) reflection in the x-axis and the
y-axis 
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2.
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a) Sketch the graph of  for each base function. i)  ii)  iii)  b) Write the equation for
g( x) to represent a single stretch that results in the same graph as in each function
in part a). c) Describe how each stretch affects the domain and range for each
function.
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Problem
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1.
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Consider the function  . a) Determine the equation of
each function. i)  ii) f(– x) iii)  b) Graph all four functions from part a) on the same set of axes. c)
From the graph, determine the pairs of equations that can be represented as translations of each
other. d) Describe the translation that can be applied to each pair of functions you
determined in part c) to generate the same graph.
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2.
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Consider the function  . a) State the domain and range
of the function. b) Use this information to determine the domain and range of the inverse
of the function. c) Determine the inverse of the function. d) Graph the function
and its inverse on the same set of axes (include the line y = x to verify the inverse).
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3.
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The value, V, in thousands of dollars, of a certain car after t
years can be modelled by the equation  . a) Sketch the graph of this relation using
transformations of the function  . b) What is the initial value of this
car? c) What is the projected value of this car after 2 years?
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