# Finding the domain and range of a linear function

## Determining the Domain and Range for Linear Functions Given a real-world situation that can be modeled by a linear function or a graph of a linear function, determine and represent a reasonable domain and range of.

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What is a domain? What is a range? Why are they important? How can we determine the domain and range for a given function? It is the set of all values for which a function is mathematically defined. It is quite common for the domain to be the set of all real numbers since many mathematical functions can accept any input. For example, many simplistic algebraic functions have domains that may seem… obvious.

Pictures make it easier to visualize what domain and range are, so we will show how to define the domain and range of functions given their graphs. This is a linear function. Remember that linear functions are lines that continue forever in each direction. Any real number can be substituted for x and get a meaningful output. For any real number, you can always find an x value that gives you that number for the output. The domain and range are all real numbers. For the examples that follow, try to figure out the domain and range of the graphs before you look at the answer.

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Given a real-world situation that can be modeled by a linear function or a graph of a linear function, determine and represent a reasonable domain and range of the linear function by using inequalities. Given a verbal statement or a graph of a linear function, determine its domain and range. Which variable is the dependent variable? To determine the domain of a given situation, identify all possible x -values, or values of the independent variable. To determine the range of a given situation, identify all possible y -values, or values of the dependent variable. Example 1 A clown at a birthday party can blow up five balloons per minute. Find the domain and range of the relations.

## Domain and Range

Domain and Range of Linear Functions

## Domain and Range of Linear and Quadratic Functions

Before we proceed, I also would like to let you know that I have a separate lesson on how to find the domain and range of radical and rational functions. The domain of a function is the set of all allowable values of the independent variable, commonly known as the x-values. The range of a function is the set of output values when all x-values in the domain are evaluated into the function, commonly known as the y-values. This means I need to find the domain first in order to describe the range. To find the range is a bit trickier than finding the domain. Since there are no x-values that can make the function to output invalid results, I can easily claim that the domain is all x values. However, it is much better to write it in set notation or interval notation. Domain and Range of Linear Functions. Author: Paige Eslick.

Domain and Range of Linear and Quadratic Functions. Let's start this lesson by having an overview of the meanings of the math terms domain and range before .
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