Average Rate of Change Flashcards
(26 cards)
What is the average rate of change of a function?
The average rate of change of a function over an interval is the change in the function’s value divided by the change in the input value.
True or False: The average rate of change can be found using the formula (f(b) - f(a)) / (b - a).
True
Fill in the blank: The average rate of change is calculated over a specific _______.
interval
If f(x) = x^2, what is the average rate of change from x = 1 to x = 3?
The average rate of change is 4.
What does a positive average rate of change indicate?
It indicates that the function is increasing over the interval.
What does a negative average rate of change indicate?
It indicates that the function is decreasing over the interval.
In the context of polynomials, what is the average rate of change between x = a and x = b?
It is calculated as (P(b) - P(a)) / (b - a) where P is the polynomial function.
True or False: The average rate of change is the same as the instantaneous rate of change.
False
What is the average rate of change of the function f(x) = 3x + 2 from x = 2 to x = 5?
The average rate of change is 3.
Define the term ‘slope’ in relation to average rate of change.
Slope refers to the average rate of change between two points on a line or curve.
Calculate the average rate of change of f(x) = x^3 from x = 1 to x = 2.
The average rate of change is 5.
Fill in the blank: The average rate of change can be visualized as the _______ of the secant line connecting two points on the graph.
slope
What is the average rate of change of the polynomial f(x) = x^4 from x = 0 to x = 1?
The average rate of change is 1.
True or False: The average rate of change can be negative, positive, or zero.
True
If a polynomial function is constant, what is its average rate of change?
The average rate of change is 0.
What is the average rate of change of the function f(x) = -2x + 5 from x = 4 to x = 6?
The average rate of change is -2.
Fill in the blank: The average rate of change is used to determine how a function behaves _______.
over an interval
In algebra, what does the term ‘difference quotient’ refer to?
It refers to the formula used to calculate the average rate of change.
What is the average rate of change of f(x) = 2x^2 - 3 from x = 1 to x = 3?
The average rate of change is 6.
True or False: The average rate of change is always equal to the derivative at a point.
False
What is the average rate of change of a linear function?
The average rate of change of a linear function is constant.
Calculate the average rate of change of f(x) = 4x - 1 from x = -2 to x = 2.
The average rate of change is 2.
Fill in the blank: The average rate of change can be thought of as the _______ of the output values divided by the change in input values.
ratio
What is the importance of the average rate of change in calculus?
It helps in understanding the behavior of functions and is foundational for the concept of derivatives.
