NAME: _______________________
DATE: ________________
Applied Math 40S
Unit Test – Polynomial Functions and Exponential Function
50
There are two parts of this unit test.
Part I: Multiple Choice
Identify the choice that best completes the statement or answers the question. Each question is worth one
mark.
1. Determine the degree of this polynomial function:
f(x) =
A.
B.
C.
D.
x3 + 6x – 8
0
1
2
3
2. Determine the leading coefficient of this polynomial function: (hint: re-write in standard
format)
f(x) = x2(x – 2x + 10)
A.
B.
C.
D.
0
1
–1
–2
3. Fill in the blanks to describe the end behaviour of this polynomial function:
The curve extends from quadrant ____ to quadrant ____.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
A.
B.
C.
D.
II; I
II; IV
III; I
III; IV
1
NAME: _______________________
DATE: ________________
4. Determine the equation of this polynomial function:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
f(x) = –x2 – 3x – 1
g(x) = x2 – 2x + 1
h(x) = –x3 – 2x2 + 1
j(x) = x3 + 2x
A.
B.
C.
D.
5. Describe the characteristics of the trend in the data.
20
y
18
16
14
12
10
8
6
4
2
2
A.
B.
C.
D.
4
6
8
10
12
14
16
18
x
increasing
decreasing
constant
no trend
6. Determine the equation of the linear regression function for the data.
x
2
5
8
10
12
14
y
135
120
115
102
92
85
A.
B.
C.
D.
17
78
20
64
y = 135 – 5x
y = 139.5 – 4.5x
y = 141.8 – 3.9x
y = 142.7 – 3.2x
2
NAME: _______________________
DATE: ________________
7. Determine the equation of the quadratic regression function for the data.
x
10
11
12
13
14
15
16
y
156
135
128
123
134
147
170
A.
B.
C.
D.
y = 4.2x2 – 107x + 803.5
y = 4.2x2 – 107x + 508.5
y = –4.2x2 – 107x + 803.5
y = –4.2x2 – 107x + 508.5
8. Use quadratic regression to interpolate the value of y when x = 5.
x
0
2
3
3
4
6
7
y
17.5
30.3
30.8
31.5
25.0
8.3
–7.6
A.
B.
C.
D.
7
–9.1
17.1
18.1
19.1
20.1
9. Which option best describes the behaviour of the exponential function f(x) =
A.
B.
C.
D.
17
203
?
increasing because a > 1
decreasing because 0 < a < 1
increasing because b > 1
decreasing because 0 < b < 1
10. How many x-intercepts does the exponential function f(x) = 2(10)x have?
A.
B.
C.
D.
0
1
2
3
3
NAME: _______________________
DATE: ________________
Part II: Open Response
1. Determine the following characteristics of the polynomial function f(x) = 15 – 2x2,
• number of x-intercept(s).
• y-intercept
• end behaviour
• domain
• range
• number of turning point(s)
[3 marks]
2. Identify the correct polynomial function for this graph. Justify your reasoning with two
explanations.
[3 marks]
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
i) y = – x + 1
iv) y = –
ii) y = –x2 + x + 4
1
iii) y = 𝑥 3 − 2𝑥 2
v) y = 2(x – 2)(x – 1)
2
vi) y =
–x
1
1
x3 +3 x + 3
Justification 1:
Justification 2:
4
NAME: _______________________
DATE: ________________
3. Write an equation for a polynomial function that satisfies each set of characteristics.
a) extending from quadrant II to quadrant IV, y-intercept of -6, not a straight line. [1 mark]
b) decreasing function, degree 1, y-intercept of 2.
[1 mark]
c) two turning points, y-intercept of 7.
[1 mark]
4. Sketch possible graphs of polynomial functions that satisfies each set of characteristics.
a) Two turning points, negative leading coefficient, constant term 3.
[2 marks]
b) Range of 𝑦 ≤ −1, constant term −4, one turning point.
[2 marks]
Ans:
a)
b)
5
NAME: _______________________
DATE: ________________
5. Which exponential function matches each graph below? Provide your reasoning. [4 marks]
i)
iii)
iv)
ii)
a)
b)
y
y
5
5
4
4
3
3
2
2
1
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
–5
Justification 1:
Justification 2:
6
NAME: _______________________
DATE: ________________
6. The table shows the number of males who entered a trade program in Canada in the odd
numbered years after 1990.
Years after 1990
1
3
5
7
9
11
Number of Males
184705
160020
151945
157875
170710
195220
Statistics Canada
a) Using technology to create a scatter plot, then determine the equation for the quadratic
regression function that models the data. Round all values to the nearest hundredth.
[2 marks]
b) Use your equation to interpolate the number of males enrolled 4 years after 1990.
[2 mark]
7
NAME: _______________________
DATE: ________________
7. A large bicycle retailer collects data on the number of bicycles in each store compared to
floor space of each store. The data is given in the table below.
Number of
Bicycles
Floor Space
(sq ft)
60
56
208
52
70
55
1400
1140
3250
1100
1500
1280
a) Determine the equation of the linear regression function. Round all values to the nearest
hundredth.
[2 marks]
b) What do the slope and x-intercept represent in this context?
c) Estimate the number of bicycles in a store with 2500 sq ft of floor space.
[2 marks]
[2 marks]
8
NAME: _______________________
DATE: ________________
8. The number of elk living in a national park can be modelled by the exponential equation
where y represents the number of elk and x represents the time, in years, after 2010.
a) Is the elk population increasing or decreasing? Explain how you know.
[2 marks]
b) What does the constant term represent? Explain how you know.
[2 marks]
c) Estimate the elk population in 2030. Show your work.
[2 marks]
9
NAME: _______________________
DATE: ________________
9. The population of a town has been growing exponentially. The data table shows the town
population in thousands over a 50 year period.
Year
Year since
1960
Population
(thousands)
1960
1970
1980
1990
2000
2010
71.1
95.6
128.2
173.2
232.4
311.8
a) Complete the table for year since 1960.
[1 mark]
b) Use exponential regression to model the population growth using year since 1960 for L1, and
population for L2. Round all values to the nearest hundredth.
[2 marks]
c) Estimate the population of the town in 1950, to the nearest hundred people. Show your work.
[2 marks]
d) Estimate in what year that the town will have a population of 564.5 thousand. Show your
work.
[2 marks]
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