AP PreCalculus Flashcards: Change in Tandem
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.
If a function's rate of change is decreasing over an interval, what is the concavity of its graph?
If the rate of change is decreasing, the graph of the function is concave down on that interval.
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If a function's rate of change is decreasing over an interval, what is the concavity of its graph?
If the rate of change is decreasing, the graph of the function is concave down on that interval.
What is a primary method for representing two quantities that vary with respect to each other in a real-world scenario?
A primary method is to construct a graph where each axis represents one of the quantities, visually showing how they change in tandem.
If a function's rate of change is increasing over an interval, what is the concavity of its graph?
If the rate of change is increasing, the graph of the function is concave up on that interval.
When is the graph of a function 'concave down'?
The graph of a function is concave down on intervals where its rate of change is decreasing.
The price of a stock is rising, but the daily gains are getting smaller each day. Is the graph of the stock price vs. time increasing or decreasing? Is it concave up or concave down?
The function is increasing because the price is rising. It is concave down because the rate of change (daily gains) is decreasing.
When is the graph of a function 'concave up'?
The graph of a function is concave up on intervals where its rate of change is increasing.
What must be true for every input value in a valid function?
For a relation to be a function, every input value must be mapped to exactly one, and only one, output value.
What is the key difference between a function that is concave up and one that is concave down, in terms of its rate of change?
For a concave up function, the rate of change is increasing, while for a concave down function, the rate of change is decreasing.
What does it mean for a function to be 'increasing' over an interval?
A function is increasing over an interval if its output values always increase as its input values increase across that interval.
How can you describe the way input and output values of a function vary together?
You can describe how they vary together by comparing function values at different inputs to see if the outputs increase, decrease, or stay the same as the inputs increase.
What is a function?
A function is a mathematical relation that maps a set of input values to a set of output values, ensuring that each input is mapped to exactly one output.