MHF4U
Name: Liam Hilson___________________
Test #1 – Polynomial Functions
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1.
a. quartic function
b. cubic function
is called a:
____
2.
a.
b.
c.
d.
____
3.
The equation of the cubic function to the right definitely has:
a. a negative first coefficient
c. an even first coefficient
b. a positive first coefficient
d. an odd first coefficient
____
4.
The cubic function to the right:
has two turning points
has one local maximum and one local minimum
increases, then decreases and increases again
all of the above
A possible equation of a cubic function with zeros at –2, 0, and 4 and end behaviour as
x → −∞, f ( x) → ∞ is:
a. f(x) = x(x – 2)(x + 4)
b. f(x) = –x(x – 2)(x + 4)
____
c. quadratic function
d. unit
5.
c. f(x) = x(x + 2)(x – 4)
d. f(x) = –x(x + 2)(x – 4)
Which function(s) has (have) opposite end behaviours?
a. f(x)
b. g(x)
c. h(x)
d. all of them
____
6.
The equation of a quartic function f(x) with zeros –2, 0, 1, 4 and such that f(x) → ∞ as x → ∞ is:
a. f(x) = x(x – 2)(x + 1)(x + 4)
c. f(x) = x(x + 2)(x – 1)(x – 4)
b. f(x) = –x(x – 2)(x + 1)(x + 4)
d. f(x) = –x(x + 2)(x – 1)(x – 4)
____
7.
f(x) = –2x(x – 1)(x – 2)(x + 2) and g(x) = –2x(x – 1)(x + 2)2 have the same:
a. number of zeros
c. fourth finite difference
b. intervals of increase and decrease
d. maximum value
____
8.
The equation of f(x) to the right, is:
a. f(x) = k(x – 1)(x – 2)(x + 2)2
b. f(x) = k(x + 1)(x + 2)(x – 2)2
____
9.
For the polynomial function to the right, when x > 2, the instantaneous rate of change is :
a. Positive
c. Negative
b. Zero
d. Cannot be determined
____
For the function f ( x) = x 3 + 2 x , determine the average rate of change of f (x) over
the interval 1 ≤ x ≤ 3.
a) -30
b) -2
c) 2
d) 158.
10.
c. f(x) = k(x + 1)(x + 2)(x – 2)
d. f(x) = k(x – 1)(x – 2)(x + 2)
/10-K
MHF4U
Name: Liam Hilson___________________
Short Answer
1. For the function: f ( x) = −2( x − 1) 2 ( x + 2)( x − 4)
a) State: the degree of the function ________
/8-K
the zeroes _____________________
the number of turning points _______
the end behaviour of this function,
as x→ -∞ ,_____________________
as x→ ∞ ,_______________________
b) Sketch the function using the above information:
2. Determine the equation of the following function.
/4-A
3. Sketch the graph of a polynomial function that satisfies each set of conditions.
/6-A
a) degree 3, negative leading
coefficient, 1 zero, no turning points
b) degree 4 positive leading
c) degree 4, 2 zeros, 3 turning
coefficient, 1 zero, 3 turning points points, Range = {y ≤ 5, y ∈ R}
MHF4U
Name: Liam Hilson___________________
4. a) Use finite differences to determine the degree of the polynomial function represented by the
following table of values.
0
1
2
3
4
5
6
7
x
/2-K
y
800
799
782
737
652
515
314
37
b) Determine the value of the leading coefficient.
/2-K
5. Indicate whether each of the following statements are true or false. For those statements that are false,
explain why the statement is false and provide an example illustrating why the statement is false.
/4-K
a) The graph of any quintic has a maximum of four turning points.
b) A polynomial function with a positive leading coefficient always starts off decreasing.
/4-C
c) A polynomial function with an odd degree must have at least one zero.
d) A polynomial function with even degree and a negative leading coefficient has end behaviours that
are different.
MHF4U
Name: Liam Hilson___________________
6. Suppose the revenue, R, in dollars, from the sales of x MP3 players is given by:
R ( x) = x(350 − 0.000325 x 2 )
a) Find the average rate of change of revenue from selling from 100 to 200 MP3 players.
/2-A
b) Estimate the instantaneous rate of change of revenue from the sale of 200 MP3 players.
/4-A
FORM
/4-C
K
/26
C
/8 A
/16
TOTAL
/50