User: You are given access to make searches on the Internet. The format for making a search is: 1. The user sends a message. 2. You will decide whether to make a search. If you choose to make a search, you will output a single message, containing the word 
 (EXACTLY AS IT IS GIVEN TO YOU), followed by ONLY your web search query. After outputting your search query, you MUST output the token 
 (EXACTLY AS IT IS GIVEN TO YOU) to denote the end of the search query. Keep your search query concise as there is a 400 characters limit.
The system will then append the web search results at the end of the user message, starting with the token 
. Take note that the user CANNOT ACCESS the content under 
 - YOU should incorporate these results into your response. Additionally, If the token 
 is present in the user's message, then you MUST NOT request another web search.

IMPORTANT! You should choose to search the web ONLY if ANY of the following circumstances are met:
1. User is asking about current events or something that requires real-time information (news, sports scores, 'latest' information, etc.)
2. User is asking about some term you are unfamiliar with (e.g. if it's a little-known term, if it's a person you don't know well, etc.)
3. User is asking about anything that involves numerical facts (e.g. distances between places, population count, sizes, date and time, etc.)
4. User explicitly asks you to search or provide links to references.
If the user's query does NOT require a web search, YOU MUST NEVER run one for no reason.
However, NEVER refuse to search the web if the user asks you to provide such information.

When using web search results, you are encouraged to cite references where appropriate, using inline links in standard markdown format.
You are also allowed to make use of web search results from previous messages, if they are STRONGLY RELEVANT to the current message.

When you are not running a web search, respond completely as per normal - there is NO NEED to mention that you're not searching. 
Do your best to be informative. However, you MUST NOT make up any information. If you think you might not know something, search for it.

Assistant: Understood. I will strictly follow these instructions in this conversation.
User: find the range of y = (x+2) + 3 / (x - 1)


 for "find the range of y = (x+2) + 3 / (x - 1)":

1.
URL: https://www.mathway.com/Calculator/domain-range-calculator
Title: Domain and Range Calculator - Mathway
Content: <b>The</b> Domain and <b>Range</b> Calculator <b>finds</b> all possible <b>x</b> and <b>y</b> values for a given function. Step 2: Click the blue arrow to submit. Choose "<b>Find</b> <b>the</b> Domain and <b>Range</b>" from the topic selector and click to see the result in our Calculus Calculator ! Examples . <b>Find</b> <b>the</b> Domain and <b>Range</b> <b>Find</b> <b>the</b> Domain <b>Find</b> <b>the</b> <b>Range</b>. Popular Problems . <b>Find</b> <b>the</b> ...

2.
URL: https://www.symbolab.com/solver/function-range-calculator
Title: Functions Range Calculator - Symbolab
Content: Free functions <b>range</b> calculator - <b>find</b> functions <b>range</b> step-by-step

3.
URL: https://www.wolframalpha.com/calculators/domain-range-calculator
Title: Domain and Range Calculator: Step-by-Step Solutions - Wolfram|Alpha
Content: Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for the domain and <b>range</b>. domain of log(x) (x^2+1)/(x^2-1) domain; <b>find</b> <b>the</b> domain of 1/(e^(1/x)-1) function domain: square root of cos(x) log(1-x^2) domain; <b>range</b> <b>of</b> arccot(x) View ...

4.
URL: https://byjus.com/domain-and-range-calculator/
Title: Domain and Range Calculator- Free online Calculator - BYJU&#x27;S
Content: <b>The</b> procedure to use the domain and <b>range</b> calculator is as follows: Step <b>1</b>: Enter the function in the input field. Step 2: Now click the button "Calculate Domain and <b>Range</b>" to get the output. Step <b>3</b>: Finally, the domain and <b>range</b> will be displayed in the new window.

5.
URL: https://www.mathway.com/popular-problems/Precalculus/457417
Title: Find the Domain and Range y=1/(x+3) - Mathway
Content: Precalculus. <b>Find</b> <b>the</b> Domain and <b>Range</b> y=1/ (x+3) <b>y</b> <b>=</b> <b>1</b> <b>x</b> <b>+</b> <b>3</b> <b>y</b> <b>=</b> <b>1</b> <b>x</b> <b>+</b> <b>3</b>. Set the denominator in <b>1</b> x+3 <b>1</b> <b>x</b> <b>+</b> <b>3</b> equal to 0 0 to <b>find</b> where the expression is undefined. x+3 <b>=</b> 0 <b>x</b> <b>+</b> <b>3</b> <b>=</b> 0. Subtract <b>3</b> <b>3</b> from both sides of the equation. <b>x</b> <b>=</b> −<b>3</b> <b>x</b> <b>=</b> - <b>3</b>. <b>The</b> domain is all values of <b>x</b> <b>x</b> that make the expression defined. Interval Notation:

6.
URL: https://www.mathway.com/popular-problems/Calculus/522725
Title: Find the Range y=x/ (x-1) | Mathway
Content: <b>y</b> <b>=</b> <b>x</b> <b>x</b> − <b>1</b> <b>y</b> <b>=</b> <b>x</b> <b>x</b> - <b>1</b>. <b>The</b> <b>range</b> is the set of all valid <b>y</b> <b>y</b> values. Use the graph to <b>find</b> <b>the</b> <b>range</b>. Interval Notation: (−∞,1)∪(1,∞) (- ∞, <b>1)</b> ∪ (<b>1</b>, ∞) Set -Builder Notation: {y|y <b>≠</b> <b>1</b>} {<b>y</b> | <b>y</b> <b>≠</b> <b>1</b>} Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by ...

7.
URL: https://www.symbolab.com/solver/range-calculator
Title: Range Calculator - Symbolab
Content: Free <b>Range</b> Calculator - <b>find</b> <b>the</b> <b>Range</b> <b>of</b> a data set step-by-step

8.
URL: https://www.desmos.com/calculator
Title: Graphing Calculator - Desmos
Content: Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

9.
URL: https://www.intmath.com/functions-and-graphs/2a-domain-and-range.php
Title: Domain and Range of a Function - Interactive Mathematics
Content: Example <b>3</b>. <b>Find</b> <b>the</b> domain and <b>range</b> <b>of</b> <b>the</b> function `f(x)=sqrt(x+2)/(x^2-9),` without using a graph. Solution. In the numerator (top) of this fraction, we have a square root. To make sure the values under the square root are non-negative, we can only choose `x`-values grater than or equal to -2.

10.
URL: https://mathcracker.com/how-to-find-range
Title: How to Find Range of a Function - MathCracker.com
Content: This is THE way you <b>find</b> <b>the</b> <b>range</b>. Pay attention: Say that we need to get the <b>range</b> <b>of</b> a given function \ (f (<b>x</b>)\). Then, we will consider a generic real number \ (<b>y</b>\) and we will try to solve for \ (<b>x</b>\) <b>the</b> following equation: \ [f (<b>x</b>) <b>=</b> <b>y</b>\] We need to determine for which values of \ (<b>y</b>\) <b>the</b> above equation can be solved for \ (<b>x</b>\). That is it.

11.
URL: https://socratic.org/algebra/expressions-equations-and-functions/domain-and-range-of-a-function
Title: Domain and Range of a Function - Algebra - Socratic
Content: <b>y</b> <b>=</b> 3x <b>+</b> <b>1</b>, <b>y</b> <b>=</b> #x^2+3x <b>+</b> 2#, and <b>y</b> <b>=</b> #x^3#. Do you notice that each one of those functions has powers of <b>x</b> that are Whole numbers? Stick with those, and you will have a polynomial. All polynomials have a domain of "All Real Numbers". In interval notation, we write: #(-\infty,\infty)#. On the horizontal number line, that covers all numbers from ...

12.
URL: https://www.mathway.com/Calculator/find-the-domain
Title: Find the Domain Calculator - Mathway
Content: Step <b>1</b>: Enter the Function you want to domain into the editor. The domain calculator allows you to take a simple or complex function and <b>find</b> <b>the</b> domain in both interval and set notation instantly. Step 2: Click the blue arrow to submit and see the result! The domain calculator allows to <b>find</b> <b>the</b> domain of functions and expressions and receive ...

13.
URL: https://byjus.com/question-answer/range-of-the-function-f-x-frac-x-2-x-2-x-2-x-1-11/
Title: Range of the function fx=x2+x+2/x2+x+1 ; x ∈ R isA. 1, ∞B. 1, 11/7C. 1 ...
Content: Adaptive Q9. <b>Range</b> <b>of</b> <b>the</b> function fx=x2+x+2/x2+x+1 ; <b>x</b> ∈ R isA. <b>1</b>, ∞B. <b>1</b>, 11/7C. <b>1</b>, 7/3.D. <b>1</b>, 4/5.

14.
URL: https://www.wikihow.com/Find-the-Range-of-a-Function
Title: How to Find the Range of a Function: Tutorial + Examples - wikiHow
Content: Categories: Mathematics. To <b>find</b> <b>the</b> <b>range</b> <b>of</b> a function in math, first write down whatever formula you're working with. Then, if you're working with a parabola or any equation where the x-coordinate is squared or raised to an even power, use the formula -b divided by 2a to get the <b>x</b>- and then y-coordinates.

15.
URL: https://www.symbolab.com/solver/function-domain-and-range-calculator
Title: Functions Domain &amp; Range Calculator - Symbolab
Content: Free functions domain and <b>range</b> calculator - <b>find</b> functions domain and <b>range</b> step-by-step


Assistant: