#1
What does a positive average rate of change indicate for a polynomial function?
The function is increasing.
ExplanationFunction values are rising over the interval.
#2
What is the formula for calculating the average rate of change of a polynomial function?
(f(b) - f(a)) / (b - a)
ExplanationDifference in function values divided by the difference in inputs.
#3
Which of the following represents the average rate of change of a polynomial function over the interval [a, b]?
(f(b) - f(a)) / (b - a)
ExplanationDifference in function values divided by the difference in inputs.
#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.
ExplanationFunction values are consistently dropping.
#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.
ExplanationIt quantifies how function values alter across the interval.
#6
What is the average rate of change of the function f(x) = 2x^3 - 5x^2 + 3x - 1 over the interval [-1, 2]?
4
ExplanationThe function's values increase by 4 units per unit change in input.
#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 may have both increasing and decreasing parts on the interval.
ExplanationThe function's values could rise and fall within the interval.
#8
For a polynomial function, when is the average rate of change equal to the instantaneous rate of change?
At any point
ExplanationAt every point within the interval.
#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 is constant over the interval.
ExplanationFunction values remain consistent 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?
[2, 4]
ExplanationThe steepest change in function values occurs over this interval.
#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 decreasing over the interval.
ExplanationFunction values consistently decline over the interval.
#12
For which type of polynomial function is the average rate of change always constant over any interval?
Linear
ExplanationConstant slope means constant average rate of change.
#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 is constant over the interval.
ExplanationNo net change in function values implies constancy.