AP PreCalculus Flashcards: Rates of Change
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What condition must be met for an average rate of change to be a good approximation of the rate of change at a point?
The average rate of change must be calculated over a sufficiently small interval containing that point.
Card 1 of 11
All Flashcards (11)
What condition must be met for an average rate of change to be a good approximation of the rate of change at a point?
The average rate of change must be calculated over a sufficiently small interval containing that point.
What is the key difference between an 'average rate of change' and a 'rate of change at a point'?
Average rate of change applies to an interval between two points, while the rate of change at a point applies to a single, instantaneous point.
A function has a positive rate of change. If the input quantity decreases, what happens to the output quantity?
The output quantity will also decrease, as a positive rate of change means both quantities change in the same direction.
What does a positive rate of change indicate about the relationship between two quantities?
A positive rate of change indicates that as one quantity increases or decreases, the other quantity does the same.
How can the rates of change at two different points be compared?
They can be compared by using average rate of change approximations over sufficiently small intervals containing each point.
What is the primary goal of analyzing how two quantities vary together in a function?
The goal is to describe their relationship at different points and over different intervals of the function.
What is the average rate of change of a function over an interval?
It is the constant rate of change that yields the same change in the output values as the function yielded on that interval of the function's domain.
What does the rate of change of a function at a single point quantify?
It quantifies the rate at which output values would change were the input values to change at that specific point.
Define 'Rate of change at a point'.
It is the rate that quantifies how output values would change if the input values were to change at that specific point.
If you need to approximate the rate of change at a specific point, what method can you use?
You can calculate the average rate of change over a sufficiently small interval that contains the point.
How can you use average rates of change to determine where a function is changing faster?
Compare the average rates of change over small, similar-sized intervals around two different points; the larger rate indicates where the function is changing faster.