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Functions: FAQ

Frequently asked questions about functions

What is a function?

A function is a mathematical rule that matches inputs to outputs. We can think of it like a machine: put a number in, the machine does some calculations, and out pops a corresponding number.
Inputs and outputs don't have to be numbers. Functions themselves can be inputs and outputs.
Learn more with our What is a function video.

Where do we use the topics from this unit in the real world?

Functions are used in all sorts of real-world applications! For example, we use functions to model physical processes, like the motion of a car or the growth of a population. We can also use them to analyze data, like finding the rate of change of a company's profits over time.

What's the difference between the domain and range of a function?

The domain is the set of all possible inputs that the function can take, while the range is the set of all outputs the function can produce.

How do we determine if a given relationship is a function?

To be a function, every input must correspond to exactly one output. If we find an input that has two different outputs, then we know that the relationship is not a function.

How do we use function notation?

Function notation is a shorthand way of expressing a function. Instead of writing out the equation every time, we can use a letter (usually f) to represent the function, and write f(x) to indicate that we are plugging in the value x as the input.

What's the difference between absolute and relative maxima and minima points?

An absolute maximum or minimum is the highest or lowest point on the entire function. A relative maximum or minimum is the highest or lowest point within a given interval, but not necessarily the entire function. These points can be important for understanding the behavior of a function.

What does it mean when we say a function is increasing or decreasing?

A function is increasing over an interval if the outputs get larger as the inputs increase. A function is decreasing if the outputs get smaller as the inputs increase.

What is the average rate of change?

The average rate of change is a measure of how much a function changes over a given interval. To calculate it, we divide the change in output by the change in input.

What are inverse functions?

Inverse functions are functions that "undo" each other. If we plug the output of one function into the inverse function, we get back the original input.

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