Name: ________________________ Class: ___________________ Date: __________ ID: A
1
It's the FUNctions Review Package!
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine the leading coefficient of this polynomial function:
f(x) =
1
2
x
3
+ 6x – 8
A.
1
2
B. 6 C. –8 D. 0
____ 2. Determine the degree of this polynomial function:
f(x) =
1
2
x
3
+ 6x – 8
A. 0 B. 1 C. 2 D. 3
____ 3. The path of a shot put thrown at a track and field meet is modelled by the quadratic function
h(d) = –0.048(d
2
– 20.7d – 26.28)
where h is the height in metres and d is the horizontal distance in metres.
Determine the height of the discus when it has travelled 10 m horizontally.
A. 6.2 m B. 6.4 m C. 6.6 m D. 6.8 m
____ 4. The distance a marathon runner covers can be modelled by the function
d(t) = 153.8t + 86
where d represents the distance in metres and t represents the time in minutes.
Approximately how far has she run after the first hour?
A. 93 km B. 3 km C. 14 km D. 9 km
Name: ________________________ ID: A
2
____ 5. Determine the equation of this polynomial function:
A. f(x) = –x
2
– 3x – 1 B. g(x) = x
2
– 2x + 1 C. h(x) = –x
3
– 2x
2
+ 1 D. j(x) = x
3
+ 2x
____ 6. Determine the equation of this polynomial function:
A. f(x) = –x
2
– 3x – 1 B. g(x) = x
2
– 2x + 1 C. h(x) = –x
3
– 2x
2
+ 1 D. j(x) = x
3
+ 2x
____ 7. How many x-intercepts does the exponential function f(x) = 2(10)
x
have?
A. 0 B. 1 C. 2 D. 3
____ 8. Determine the equation of this polynomial function:
A. f(x) = –x
2
– 3x – 1 B. g(x) = x
2
– 2x + 1 C. h(x) = –x
3
– 2x
2
+ 1 D. j(x) = x
3
+ 2x
Name: ________________________ ID: A
3
____ 9. Identify the range of the exponential function y = 10
x
.
A. {y | y < 0, y R} B. {y | y > 0, y R} C. {y | y 0, y R} D. {y | y R}
____ 10. Match the following graph with its function.
A. y =
2
5
2
x
B. y =
5
2
2
x
C. y =
2
5
1
2
x
D. y =
5
2
1
2
x
____ 11. Determine the y-intercept of the exponential function h(x) = e
x
.
A. 0 B. 1 C. 2 D. 4
____ 12. The following data set involves exponential growth. Determine the missing value from the table.
x 0 1 2 3 4 5 6 7
y 3 6 12 24 48 192 384
A. 72 B. 96 C. 104 D. 144
Short Answer
1. How many x-intercepts might a degree 2 polynomial function have?
2. Describe the end behaviour of this polynomial function:
f(x) = –5x
2
+ x – 2
3. Determine if the data in the table represents an exponential function. Provide your reasoning.
x 0 1 2 3 4 5
y 2 4 8 16 32 64
4. Sketch the exponential function f(x) =
1
2
3
x
.
Name: ________________________ ID: A
4
5. Sketch the exponential function g(x) =
3
1
2
x
.
6. Write 56 = 10
y
as a logarithmic equation.
7. The altitude above sea level is modelled by the equation
A(p) = 100 610 – 21 790 ln p
where A(p) represents the altitude in feet and p represents the atmospheric pressure in kilopascals
(kPa).
Describe what the intercepts of this function mean.
Problem
1. Determine the following characteristics of the polynomial function f(x) = –5(x – 1)(x
2
+ 4).
Show your work.
• number of possible x-intercepts
• y-intercept
• end behaviour
• domain
• range
• number of possible turning points
2. Aisha screen prints T-shirts for sale at concerts. When buying blank T-shirts, the price Aisha must
pay is related to the size of the order. Four of her previous orders are listed in the table below.
Number of
Shirts
225 310 400 750
Cost per
Shirt ($)
14.90 14.56 14.20 12.80
Aisha has misplaced the information from her supplier about prices on bulk orders. Interpolate the
price per shirt if she orders 625 shirts. Show your work.
3. The number of elk living in a national park can be modelled by the exponential equation
y 145 0.985
x
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.
b) What does the constant term represent? Explain how you know.
c) Estimate the elk population in 2030. Show your work.
Name: ________________________ ID: A
5
4. Which function matches each graph below? Provide your reasoning.
i) y =
4
5
logx
iii) y =
4
5
logx
ii) y =
4 logx
iv) y =
4 logx
a) b)
5. Write an equation and sketch a graph for a polynomial function that satisfies each set of
characteristics. Explain your reasoning.
a) extending from quadrant II to quadrant IV, y-intercept of 0, not a straight line
b) extending from quadrant II to quadrant I, y-intercept of 5, no x-intercept or turning point
ID: A
1
It's the FUNctions Review Package!
Answer Section
MULTIPLE CHOICE
1. A
2. D
3. B
4. D
5. C
6. A
7. A
8. D
9. B
10. D
11. B
12. B
SHORT ANSWER
1. 0, 1, or 2
2. The curve extends from quadrant III to quadrant IV.
3. yes; each y-value is 2 times the previous one
4.
ID: A
2
5.
6. y = log 56
7. The x-intercept is 101.2. This is the atmospheric pressure at sea level, when x = 0.
There is no y-intercept because this is a logarithmic function and the atmospheric pressure never
reaches 0 kPa.
PROBLEM
1. In standard form, this function is f(x) = –5x
3
+ 5x
2
– 20x + 20.
This is a cubic function. The degree is 3.
Therefore, there are either 1, 2, or 3 possible x-intercepts.
Also, the domain and range of a cubic function are all real numbers:
Domain: {x | x R}
Range: {y | y R}
A cubic function has either 0 or 2 turning points.
The constant term is 20, so the y-intercept is 20.
The leading coefficient is negative.
Therefore, the curve extends from quadrant II to quadrant IV.
2. I used a spreadsheet to determine the equation of the linear regression function:
C = 15.80 – 0.004t
where C represents the cost per T-shirt and t represents the number of T-shirts.
C = 15.80 – 0.004t
C = 15.80 – 0.004(625)
C = 13.30
The cost per T-shirt should be about $13.30 when she orders 625 shirts.
ID: A
3
3. a) The population is decreasing because the constant term is positive and the base is between 0 and
1.
b) The constant term represents the initial population of 145 elk in 2010.
c) 2030 is twenty years after 2010, so x = 20:
y 145 0.985
x
y 145 0.985
20
y 107.174. . .
The population in 2030 is about 107 elk.
4. Graph a) is increasing. That means it must have a > 0.
Since log 10 = 1 and the value of the graph when x = 10 is 4, function ii) matches graph a).
Graph b) is decreasing. That means it must have a < 0.
Since log 10 = 1 and the value of the graph when x = 10 is about –0.8, function iii) matches graph
b).
5. a) The function extending from quadrant II to quadrant IV, so the degree is an odd number.
Also, the leading coefficient must be negative.
Since the graph is not a straight line, the degree is not 1.
The y-intercept is 0, so the constant term must be 0.
Sample function: f(x) = –x
3
b) The function extending from quadrant II to quadrant I, so the degree is an even number.
There is no turning point or x-intercept, so the degree must be 0; a constant function.
The y-intercept is 5, so this must be the constant function f(x) = 5.
