Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which of the reciprocal functions has a vertical asymptote with equation  ?
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2.
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Which rational function has the following characteristics? • a vertical
asymptote with equation  • a horizontal asymptote with equation  • a point of discontinuity at 
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3.
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What are the x-intercepts of the graph of  ? A. | 2, –7 | C. | 3, 5 | B. | –3, –5 | D. | –2, 7 |
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4.
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Given the functions  and  , determine an equation for the combined
function  .
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For the following question(s), assume that x is in radians, if
applicable.
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5.
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Given the functions  and  , what is the range of the composite
function  ? A. |  | C. |  | B. | cannot be
determined | D. |  |
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6.
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Shown is the graph of  , where  and  is a function
of the form  .
What
equation represents  ?
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7.
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Given the functions  and  , what is the value of  ?
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8.
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Given the functions  and  , what is the domain of the composite
function  ? A. |  | C. |  | B. |  | D. | cannot be
determined |
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9.
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If  and  , what is the simplified combined function
 ?
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10.
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What is the value of 4!?
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11.
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The number of different ways that 8 bikes can be locked in a bike rack is
A. | 2520 | C. | 40 320 | B. | 5040 | D. | 362 880 |
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12.
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Evaluate  . A. | 504 | C. | 120 960 | B. | 84 | D. | 60 480 |
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13.
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An orchestra has 2 violinists, 4 cellists, and 5 harpists. Assume that the
players of each instrument have to sit together, but they can sit in any position in their own group.
In how many ways can the conductor seat the members of the orchestra in a line?
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14.
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Evaluate the expression  . A. | 66 | C. | 239 500 800 | B. | 120 | D. | 132 |
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15.
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Evaluate the expression  . A. | 17 280 | C. | 151 200 | B. | 31 752 000 | D. | 3 628 800 |
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16.
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After the tryouts for the volleyball team, the coach selects 13 people to join
the team. Due to a problem with transportation, only 8 people can travel. In how many ways can the
coach pick the people to go?
A. | 104 | C. | 1287 | B. | 51 891 840 | D. | 520 |
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17.
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For a mock United Nations, 5 boys and 7 girls are to be chosen. If there are 11
boys and 9 girls to choose from, how many groups are possible?
A. | 236 880 | C. | 10 059 033 600 | B. | 16 632 | D. | 498 |
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18.
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For which of the following terms is a = 66 in the expansion of (x
+ y)12?
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19.
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Suppose that 18 non-collinear points are plotted on a plane. Which expression
represents the number of triangles that can be formed using these points?
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20.
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Solve for the variable:  A. |  | C. | 60 | B. |  | D. | 7 |
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Short Answer
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1.
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Given the functions  and  , determine a simplified equation for  .
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For the following question(s), assume that x is in radians, if
applicable.
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2.
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a) Graph the functions  and  on the grid. b)
Graph the function  on the same grid. 
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3.
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Solve for n:  .
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Problem
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1.
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a) Use the asymptotes and intercepts to make a quick sketch of the
function  and its reciprocal  on the same set of axes. b) Describe the symmetry
in the graphs in part a). c) Determine the equation of the mirror line in your graph from
part a). d) Determine intervals where f is positive and where f is negative.
Determine intervals where g is positive and where g is negative. How do the
two sets of intervals compare to each other? e) Does the pattern from part d) occur for all
pairs of functions  and  ,  ? Explain why or why
not.
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2.
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Use the graph of the combined function  to determine an
approximate solution to the inequality  . 
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