AP PreCalculus Flashcards: Implicitly Defined Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
On the graph of an implicitly defined function, two nearby points are (1, 5) and (1.1, 5.2). How are the variables varying together in this region?
Since both variables are increasing, the ratio of their change is positive, meaning they are increasing simultaneously in this region.
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On the graph of an implicitly defined function, two nearby points are (1, 5) and (1.1, 5.2). How are the variables varying together in this region?
Since both variables are increasing, the ratio of their change is positive, meaning they are increasing simultaneously in this region.
What is a primary goal when analyzing the relationship between variables in an implicitly defined function?
A primary goal is to determine how the two quantities related in the function vary together as one changes.
What is an implicitly defined function?
An implicitly defined function is a relationship described by an equation involving two variables, where one variable may not be explicitly solved in terms of the other.
In a specific region of an implicitly defined function's graph, both variables are observed to be decreasing. What can you conclude about the ratio of their change?
Since both variables are moving in the same direction (decreasing), the ratio of the change between them must be positive in that region.
Can a single equation with two variables represent more than one function?
Yes, an equation involving two variables can implicitly describe one or more functions.
How can you construct a graph for an equation involving two variables?
A graph for an equation involving two variables can be constructed by finding ordered pair solutions to the equation and plotting them on a coordinate plane.
If the ratio of change between two variables is positive, and one variable is decreasing, what must be true about the other variable?
If the ratio of change is positive, the variables move together, so the other variable must also be decreasing.
What does it mean if the ratio of the change in two variables is positive for an implicitly defined function?
If the ratio of change is positive for nearby points, it means the two variables simultaneously increase or simultaneously decrease.
How are ordered pairs on a graph related to the equation that defines it implicitly?
The ordered pairs on the graph of an implicitly defined function represent the solutions to the equation.
Implicit Relationship
An implicit relationship is one described by an equation involving two variables that has not been explicitly solved for one variable in terms of the other.