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 following functions has a slant asymptote when graphed?
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2.
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Which function has vertical asymptotes with equations  and 
 ?
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3.
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Which function has a point of discontinuity at  ?
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4.
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Which graph represents  ?
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5.
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Which function has an x-intercept of  ?
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6.
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What is the x-intercept of  ? A. | There is no x-intercept. | C. |  | B. |  | D. | 0 |
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7.
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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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8.
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What is the equation for the horizontal asymptote of the graph of the function
shown? 
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9.
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Solve the equation  . A. | x =  | C. | x =
–6 | B. | x = –8 | D. | x =  |
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10.
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Solve the equation  . A. | x =  | C. | x =  | B. | x = 3 | D. | x = 4 |
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Short Answer
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1.
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Sketch the graph of the function  using transformations and
identify a) the vertical asymptotes (if any) b) the horizontal asymptotes (if
any) c) the domain and range d) the behaviour near any non-permissible
values e) the end behaviour 
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2.
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Determine the approximate slope of the tangent to the curve  at  , to
one decimal place.
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3.
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Consider the function  . a) Determine the key features
of the function: i) domain and
range ii) intercepts
iii) equations of any asymptotes b) Sketch the graph of the function.
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Problem
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1.
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A photographer uses a light meter to measure the intensity of light from a flash
bulb. The intensity, I, in lux, of the flash bulb is a function of the distance, d, in
metres, from the light and can be represented by  . a) Determine the following,
to two decimal places: i) the intensity of light 3 m from
the flash bulb ii) the average rate of change in the
intensity of light for the interval  b) What does the sign of your answer to part
a)ii) indicate about the light intensity?
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2.
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The population, P, of a small town is modelled by the function  ,
where t is time, in years, since the start of 1990. a) Is the population increasing
or decreasing? Justify your answer. b) The town will need its own transit system if the
population exceeds 50 000. Will the town’s population ever exceed 50 000? Explain.
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