#1
What does a positive average rate of change indicate for a polynomial function?
The function is decreasing.
The function is increasing.
The function is constant.
The function has no real roots.
#2
What is the formula for calculating the average rate of change of a polynomial function?
Δy / Δx
(f(b) - f(a)) / (b - a)
(f(a) - f(b)) / (a - b)
f'(x)
#3
Which of the following represents the average rate of change of a polynomial function over the interval [a, b]?
f(b) - f(a)
(f(b) - f(a)) / (b - a)
f'(x)
(b - a) / (f(b) - f(a))
#4
If the average rate of change of a polynomial function is negative over an interval, what can be said about the function?
The function is strictly decreasing over the interval.
The function is strictly increasing over the interval.
The function is constant over the interval.
There is not enough information to determine.
#5
Which of the following statements about the average rate of change of a polynomial function is true?
It measures the rate at which the function's value changes over an interval.
It is always equal to the function's derivative.
It is only defined for linear functions.
It is independent of the interval chosen.
#6
What is the average rate of change of the function f(x) = 2x^3 - 5x^2 + 3x - 1 over the interval [-1, 2]?
#7
If a polynomial function has a positive average rate of change over an interval, what can be concluded about the behavior of the function on that interval?
The function is always increasing on the interval.
The function is always decreasing on the interval.
The function may have both increasing and decreasing parts on the interval.
The function has no real roots on the interval.
#8
For a polynomial function, when is the average rate of change equal to the instantaneous rate of change?
At the point of maximum value
At the point of minimum value
At any point
Never
#9
For a polynomial function, if the average rate of change is zero over an interval, what can be said about the function?
The function has no real roots.
The function is constant over the interval.
The function is strictly increasing over the interval.
The function is strictly decreasing over the interval.
#10
Which of the following intervals will result in the largest absolute value of the average rate of change for the function f(x) = x^2 - 4x + 3?
[0, 2]
[1, 3]
[2, 4]
[-1, 1]
#11
For a polynomial function, if the average rate of change is negative over an interval, what can be said about the function?
The function is always increasing over the interval.
The function is always decreasing over the interval.
The function may have both increasing and decreasing parts on the interval.
The function is constant over the interval.
#12
For which type of polynomial function is the average rate of change always constant over any interval?
Linear
Quadratic
Cubic
Quartic
#13
If the average rate of change of a polynomial function is zero over an interval, what does this imply about the behavior of the function over that interval?
The function has no real roots over the interval.
The function is constant over the interval.
The function is strictly increasing over the interval.
The function is strictly decreasing over the interval.