May 10, 2017
NAME:
APPLIED 40S – CHAPTER 6/7
1. Which function does the graph represent?
A. y  2 x
1
x
B. y   2 
3
C. y  3x
1
D. y   
3
x
2. Use the graph below to answer the following question and select the best answer.
Which equation does the graph represent?
A. y  2 x 2  7 x  3
B. y  2 x 2  7 x  3
C. y  2 x 2  7 x  3
D. y  2 x 2  7 x  3
3. Which of the following functions has an unrestricted range, y y R?
A. exponential
B. logarithmic
C. quadratic
D. sinusoidal
4. For all the graphs, identify the kind of polynomial function, and whether the leading
coefficient is positive or negative.
(4)
5. Label the following statements true or false: (5)
___ a. All quadratic functions must have an x-intercept.
___ b. All polynomial functions must have a y-intercept.
___ c. A constant function is a vertical line.
___ d. A cubic function may extend from Quadrants I to II, or from Quadrants III to IV.
___ e. The maximum number of x-intercepts for a polynomial function is equal to the degree of
the function.
6. For an exponential function y  a  b  ,
x
a) what determines if it is increasing or decreasing?
(1 mark)
b) what determines the y-intercept?
(1 mark)
c) state the domain and range for any exponential function.
(2 marks)
7. Match each function with the corresponding graph below.
(4 marks)
a) y  0.2  0.4 
x
b) y  0.5 log x
c) y  2  4 
8. For the function y  6 log x ,
a) will it be increasing or decreasing?
(1 mark)
b) will it have an x-intercept or a y-intercept?
(1 mark)
c) state the domain and range
(2 marks)
x
d) y  2 log x
9. A population increases according to the equation y  3000 1.10x . In this context,
a) what does the “3000” represent?
(1 mark)
b) what does the “1.10” represent?
(1 mark)
10. In a diving competition, Tracy’s first dive can be modelled by the equation:
h  4.9t 2  2.72t  10
where t represents the dive time (in seconds), and h represents the diver’s height (in metres)
above the water.
How much time does it take for Tracy to reach the water? Show your work. (Include a sketch, for
example.)
(2 marks)
11. A garden was treated to control pests. Every hour after treatment, there were half as many
pests as there were the previous hour. After six (6) hours, 65 pests remained.
a) How many pests were there before treatment? Show your work.
(2 marks)
b) Which function best represents this situation?
(1 mark)
A. linear
B. quadratic
C. cubic
D. exponential
12. Bailey launched his remote control plane. He recorded the height of the plane at different
times during the flight.
a) Determine the cubic regression equation that models this data.
(1 mark)
b) Create a clearly labelled graph of the equation in (a).
(3)
c) Using your equation in (a), determine how long it will take for the plane to reach a
height of 100 ft.
(1 mark)
d) Provide one limitation of the domain.
(1 mark)
13. The Gateway Arch in St. Louis, in the United States, approximates a parabola. Steven
learns that the arch is 192 m wide. (Diagram is not drawn to scale.)
At 2.5 m from his starting point, Steven measures the height of the arch to be 10 m.
a) Determine the quadratic equation that models the shape of the arch. Show your work. (Hint:
Make your own table of values) Express all coefficients in the equation to a minimum of three
(3) decimal places.
(2 marks)
b) Calculate the arch’s maximum height.
(1 mark)
14. The ice thickness on Lake Mathitoba is measured weekly every winter. The data for
one season is shown in the table below:
a) Determine the logarithmic regression equation that models this data.
(1 mark)
b) Create a clearly labelled graph of the equation in (a).
(3)
c) It is considered safe to operate a vehicle on lake ice if it is at least 30 cm thick. Use your
equation in (a) to determine the first full day it will be safe to drive on the ice. Show
your work.
(2 marks)
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