Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The two functions in the graph shown are reflections of each other. Select the
type of reflection(s).  A | a reflection in the line y = x | C | a reflection in the
y-axis | B | a reflection in the x-axis and the y-axis | D | a reflection in the
x-axis |
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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 of the following functions is the correct inverse for the function
f( x) =   ?
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4.
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Which of the following functions is the correct inverse for the function  ,
{ x | x ³ 0, x Î R}?
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5.
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Which graph represents the inverse of the function shown? 
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6.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 3 units up | C | 3 units to the left | B | 3 units down | D | 3 units to the
right |
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7.
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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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8.
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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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9.
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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 horizontally by a factor of 1/|b| | C | f(x) is
stretched vertically by a factor of |b| | D | f(x) is stretched vertically by a
factor of |b| and reflected in the x-axis |
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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 | 9 units to the left 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 left and 9 units
down |
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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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For each function f( x), i) determine  ii)
graph f( x) and its inverse a)  b) 
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Problem
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1.
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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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2.
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In ballistics, the paths of projectiles are studied. It is known that the
greater the speed at which an object is fired, the farther it will travel. For a particular
spring-loaded cannon, this relationship can be modelled by  , where d is the distance, in
metres, travelled by the projectile and v is the muzzle speed, in metres per
second. a) Graph the distance function and state its domain and range. b) Graph
the inverse of the distance function. What does it represent? State its domain and range.
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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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