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 2 units down, 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 2 units to the right | C | a reflection in the
x-axis, a vertical translation of 2 units up, and a horizontal translation of 3 units to the
right | D | a reflection in the x-axis, a vertical translation of 3 units up, and a
horizontal translation of 2 units to the left |
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2.
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Which of the following graphs represents the graph of the function 
transformed to  ?
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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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The equation of the inverse of  is
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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 | 9 units down | C | 9 units to the right | B | 9 units up | D | 9 units to the
left |
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6.
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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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7.
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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| | B | f(x) is
stretched horizontally by a factor of 1/|b| and reflected in the y-axis | 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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8.
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Which of the graphs shown below represents the base function  and the
stretched function g( x) =  x2?
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9.
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Which of the graphs shown below represents the base function  and the
stretched function g( x) = (  x) 2?
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10.
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Compared to the graph of the base function  , the graph of the function
 is translated A | 6 units to the left and 2 units up | C | 2 units to the right and 6 units
down | B | 6 units to the right and 2 units down | D | 2 units to the left and 6 units
up |
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Short Answer
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1.
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For each of the following, describe the combination of transformations that must
be applied to the graph of  (shown in blue) to obtain the graph of g( x)
(shown in red). a)  b)  c) 
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2.
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a) Determine the inverse of the function  . b) Determine
the domain and range of the function and its inverse. c) Is the inverse a function?
Explain.
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Problem
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1.
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For the base function  , a reflection in the y-axis is
followed by a reflection in the x-axis. a) Discuss the effect of each reflection on
the base function. b) Is there a point that you expect to be invariant during these
reflections? If so, state its coordinates. c) Graph the function after each
reflection. d) Use your graph in part c) to verify your answer for part b). e)
Make a general statement regarding invariant points after reflections in the x-axis and the
y-axis.
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2.
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The base function  is reflected in the x-axis, stretched horizontally
by a factor of 2, compressed vertically by a factor of  , and translated 3 units to the left and 5
units down. a) Write the equation of the transformed function
g( x). b) Graph the original function and the transformed function on the same
set of axes. c) Which transformations must be done first but in any order? d)
Which transformations must be done last but in any order?
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3.
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Given the function  , a) determine the inverse of the
function b) graph the function and its inverse on the same set of axes
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