Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is true about the behaviour of the function  as    (right to left)? A. |  -¥ | C. |  | B. |  +¥ | D. | f(x) is
undefined |
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2.
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Which graph represents the function  ?
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3.
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Which of the following functions has a slant asymptote when graphed?
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4.
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Which graph represents  ?
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5.
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Which function has a y-intercept of  ?
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For the following question(s), assume that x is in radians, if
applicable.
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6.
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Given the functions  and  , the graph of the combined function 
most likely resembles
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7.
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Given the functions  and  , a graph of the combined function 
most likely resembles
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8.
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Given the functions  and  , the graph of the combined function 
most likely resembles
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9.
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An equation for the graph shown is most likely 
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10.
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Given the functions  and  , which of the following is most likely
the graph of  ?
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11.
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What is the x-intercept of  ? A. | There is no x-intercept. | C. |  | B. |  | D. | 0 |
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12.
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What is the value of k in the function  if its graph passes
through the point (3,  ) ? A. |  | C. | –10 | B. | 4 | D. | No such
k exists |
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13.
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Given the functions  and  , determine the equation for the combined
function  .
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14.
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Given the functions  and  , determine the domain of the combined
function  .
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15.
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If  and  , what are the restrictions on the domain
for the combined function  ?
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16.
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Solve for the variable:  = 252 A. | 15 | C. | 6 | B. |  | D. |  |
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17.
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An orchestra has 2 violinists, 3 cellists, and 4 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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18.
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Solve for n in the expression  .
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19.
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A scout troop is arranged in a circle for an opening ceremony. If there are 9
scouts, in how many unique ways can they stand around the circle?
A. | 5040 | C. | 81 | B. | 40 320 | D. | 362 880 |
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20.
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The leadership committee at a high school has 4 grade 10 students, 2 grade 11
students, and 6 grade 12 students. This year, 12 grade 10, 8 grade 11, and 10 grade 12 students
applied for the committee. How many ways are there to select the committee?
A. | 2 910 600 | C. | 733 | B. | 100 590 336 000 | D. | 163 136 |
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Short Answer
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1.
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Determine the equation(s) of the vertical asymptote(s) of the function  .
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2.
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Given the functions  and  , what is the value of  ?
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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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Expand and simplify:  .
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