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 down | C | 5 units up | B | 5 units to the right | D | 5 units to the
left |
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2.
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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 to the left | D | 9 units up |
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3.
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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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4.
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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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5.
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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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6.
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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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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, –1) | C | (0, 1) | B | (–1, 0) and (1, 0) | D | (1, –1) |
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Short Answer
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1.
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For each g( x), describe the transformation(s) from the base
function  . a)  b)  c) 
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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 each function after the
reflections. d) Use this graph 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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Draw a graph to determine the invariant points of  when it is reflected in
the a) x-axis b) y-axis
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