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## Algebra 1

### Course: Algebra 1>Unit 8

Lesson 13: Intro to inverse functions

# Functions: FAQ

## 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.

## 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, left parenthesis, x, right parenthesis 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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