# Domain & Range Homework: Difference Explained

• dranseth
In summary, the two intervals x:x\in(-\infty,\infty) but x\neq1 and x:x\in(-\infty,1)\cup(1,\infty) are not different. They both represent the whole real line except for x=1. This inconsistency may be due to missing the fact that they are equivalent.
dranseth

## Homework Statement

I don't really know how to ask this, so I'll get straight into an example.

x:x$$\in$$(-$$\infty$$,$$\infty$$) but x$$\neq$$1
x:x$$\in$$(-$$\infty$$,1)$$\cup$$(1,$$\infty$$)

what is the difference between these two intervals?

## The Attempt at a Solution

There is no difference. They are both the whole real line except for x=1. Why do you ask?

At times when I look at answers in the back of the book, it is one or the other. There didn't appear to be any consistency, so I was wondering if I was possibly missing something..

Yes, you are missing seeing that they are the same thing!

## 1. What is the difference between domain and range?

The domain of a function refers to the set of all possible input values for the independent variable, while the range refers to the set of all possible output values for the dependent variable. In simpler terms, the domain is the set of x-values and the range is the set of y-values.

## 2. How do you determine the domain and range of a function?

To determine the domain of a function, you need to look at the independent variable and identify any restrictions or limitations on its values. The range can be found by analyzing the behavior of the function as the independent variable changes. You can also create a table or graph to help visualize the values of the domain and range.

## 3. What is the importance of understanding domain and range?

Understanding domain and range is crucial in mathematics because it helps us to identify the possible inputs and outputs of a function. This information is essential in solving equations, graphing functions, and identifying any restrictions or limitations on the values of a function.

## 4. Can the domain and range of a function be infinite?

Yes, the domain and range of a function can be infinite. This means that there are no restrictions or limitations on the values of the independent or dependent variable. For example, the function y = x² has a domain and range of all real numbers, which is infinite.

## 5. How do you graph the domain and range of a function?

To graph the domain and range of a function, you can plot the points on a coordinate plane using the values of the domain as the x-coordinates and the values of the range as the y-coordinates. You can also use a graphing calculator or a computer program to create a visual representation of the domain and range.

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