Reddit
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r/learnmath on Reddit: How to find Range of function
December 8, 2020 -
Hey so, I jumped a math class and I have a big test coming. I know how to find the domain of a function without a graph, but how do you find the range? The range of a function without a graph, I mean. They discussed it in the class before this one but I wasn't there and the notes aren't telling me much. If there isn't a specific way, are there any tips or tricks? Specifically quadratic functions or functions with square roots in them? My teacher in his notes just replaces the radicand or any other number in a parentheses like thing with [0, infinity)
Top answer 1 of 2
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One way to do it is by inverting the function (swap x and y, then solve for y). The domain of the inverted function will be the range of the original function. Ex: y = x2 + 3, find domain and range This function doesn’t have anywhere where you would be dividing by 0 or taking the square root of a negative, so the domain is (-inf, inf) To find range, first invert function x = y2 + 3 => y2 = x - 3 => y = sqrt(x - 3) The range will be the domain of this inverted function. For x<3, you would be taking the square root of a negative, so the domain of the inverted function is [3, inf). That is the range of the original function.
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God bless x6
Lumen Learning
courses.lumenlearning.com › waymakercollegealgebra › chapter › find-domain-and-range-from-a-graph
Determine Domain and Range from a Graph | College Algebra
We can observe that the graph extends horizontally from [latex]-5[/latex] to the right without bound, so the domain is [latex]\left[-5,\infty \right)[/latex]. The vertical extent of the graph is all range values [latex]5[/latex] and below, so the range is [latex]\left(\mathrm{-\infty },5\right][/latex]. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range. Find the domain and range of the function [latex]f[/latex].
How to find Range of function
One way to do it is by inverting the function (swap x and y, then solve for y). The domain of the inverted function will be the range of the original function. Ex: y = x2 + 3, find domain and range This function doesn’t have anywhere where you would be dividing by 0 or taking the square root of a negative, so the domain is (-inf, inf) To find range, first invert function x = y2 + 3 => y2 = x - 3 => y = sqrt(x - 3) The range will be the domain of this inverted function. For x<3, you would be taking the square root of a negative, so the domain of the inverted function is [3, inf). That is the range of the original function. More on reddit.com
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December 8, 2020How do I calculate the range of this function?
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November 25, 2022How do you find the range of a function?
The range of a function is the y-values of the equation or graph. To find the range of the function graphically, inspect the graph from the bottom to the top. If the graph is continuous, the range is all real numbers. If there are holes or breaks in between, then the range does not include those y-values. Algebraically, the range of the graph is found by substituting the x-values into the equation and solving for y.
study.com
study.com › courses › math courses › algebra i: high school
Range of a Function | Overview, Examples & Graph | Study.com
What is the easiest way of writing the range of a function?
The easiest method of finding the range of a function, say y = f(x), is to express x as g(y) and identify the domain set for g(y). This will be the range for the given function f(x).
byjus.com
byjus.com › maths › domain-codomain-range-functions
Domain Range and Codomain Of A Function
What is range in math?
Range in math is all of the function's outputs, dependent variables, or y-values. When a function is represented as a graph, we can find its range by finding the y-values where there is a graph.
study.com
study.com › courses › math courses › algebra i: high school
Range of a Function | Overview, Examples & Graph | Study.com
Videos
How to find the range of a function (video)
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Algebra l - How to Find the Range of a Function - YouTube
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Domain and range of a function given a formula | Algebra II | Khan ...
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How do you find the range of a function?! #math #algebra #mathematics ...
Indeed
indeed.com › career-advice › career-development › how-to-find-range-of-a-function
Finding the Range of a Function: 3 Methods (With Examples) | Indeed.com
How do I choose the best method for finding the range of a function? The methods presented here have a variation that makes them suitable for different situations. You might consider how your x and y factors relate to one another to choose the best method for calculating the range of the function in your formula.
BYJUS
byjus.com › maths › domain-codomain-range-functions
Domain Range and Codomain Of A Function
August 17, 2022 - Domain restrictions refer to the values for which the given function cannot be defined. ... The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
GeeksforGeeks
geeksforgeeks.org › mathematics › domain-and-range-of-function
Domain and Range | How to Find Domain and Range of a Function - GeeksforGeeks
In this case, the domain is the set X, which is: ... Range: The range consists of the set of output values produced by the function. For f(x) = x2, we calculate the outputs for each element in the domain:
Published July 23, 2025
Cuemath
cuemath.com › calculus › domain-and-range-of-a-function
Domain and Range - From Graph | How to Find Domain and Range of a Function?
Then we get x - 2 ≠ 0. Solving this, we get x ≠ 2. Thus, its domain is the set of all real numbers except 2 which in interval notation can be written as (-∞, 2) ∪ (2, ∞). The range of a function is the set of all its outputs.
Expii
expii.com › t › finding-the-range-of-a-function-algebraically-4795
Finding the Range of a Function, Algebraically - Expii
How can values not be in the range? Values not included in range are values that are impossible given all the function's domain. They might be beyond an asymptote, or be values that the function simply skips.
Study.com
study.com › courses › math courses › algebra i: high school
Range of a Function | Overview, Examples & Graph | Study.com
The range of a function is the y-values of the equation or graph. To find the range of the function graphically, inspect the graph from the bottom to the top. If the graph is continuous, the range is all real numbers.
Mathway
mathway.com › Calculator › domain-range-calculator
Domain and Range Calculator | Mathway
Enter the formula for which you want to calculate the domain and range. The Domain and Range Calculator finds all possible x and y values for a given function.
Quora
quora.com › How-to-find-range-of-a-function-algebraically-What-is-the-formula-for-this
How to find range of a function algebraically? What is the formula for this? - Quora
Answer (1 of 5): The range is the input of a function. It is the set of all possible inputs that yield outputs of a function. The question of a function’s range is a numerical component of the behavior of a function. We want to know how a function acts when it’s inputs are small, large, zero, or ...
SQLPad
sqlpad.io › tutorial › range-calculation-r-guide
Range Calculation in R: A Guide - Learn to calculate range in R with our comprehensive guide. Perfect for beginners eager to master R programming with detailed code samples. - SQLPad.io
May 7, 2024 - The basic syntax of the range() function is quite straightforward: ... na.rm is a logical parameter that, when set to TRUE, instructs R to ignore NA (missing) values during the calculation.
Wolfram|Alpha
wolframalpha.com › calculators › domain-range-calculator
Domain and Range Calculator: Step-by-Step Solutions - Wolfram|Alpha
The values taken by the function are collectively referred to as the range. For example, the function Start Power, Start base, x , base End,Start exponent, 2 , exponent End , Power Endx2 takes the reals (domain) to the non-negative reals (range). The sine function takes the reals (domain) to the closed interval [-1, 1]-1, 1 (range). (Both of these functions can be extended so that their domains are the complex numbers, and the ranges change as well.)
Top answer 1 of 3
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Here's a method without calculus.
Let $f(x)=y=\frac{x^2+6}{2x+1}\Rightarrow 2xy+y=x^2+6\Rightarrow x^2-2xy+6-y=0\Rightarrow x=\frac{2y±\sqrt{4y^2-24+4y}}{2}$ Denominator can never be $0$ in this case. So the domain depends only upon $4y^2-24+4y\Rightarrow 4y^2+4y-24≥0\Rightarrow 4(y-2)(y+3)≥0\Rightarrow (y-2)(y+3)≥0\Rightarrow y\in(- \infty, -3]\cup[2,\infty).$
Hence the range of the $f(x)$ is $(- \infty, -3]\cup[2,\infty)$
I guess you know solving inequalities...
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To find the range of a function, my first instinct is to check whether the graph has an inverse. We can do this informally using the Horizontal Line Test. If no Horizontal Line intersects the function more than once, then the function has an inverse. With that, we can find $f(y) = x$. The "domain" of $f(y)$ would be the range of the function $f(x)$.
Else, we can use the derivatives of the function to help us find the maximum and minimum which gives us the lower and upper bound of the range of $f(x)$.
Mathematics LibreTexts
math.libretexts.org › bookshelves › algebra › college algebra 1e (openstax) › 3: functions
3.3: Domain and Range - Mathematics LibreTexts
October 6, 2021 - Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range.
IntMath
intmath.com › home › introduction to geometry › 4a. domain and range of a function
Domain and Range of a Function
After finishing this lesson head over to our interactive calculator to help you find the Domain and Range of a Fuction. ... The domain of this function is `x ≥ −4`, since x cannot be less than ` −4`. To see why, try out some numbers less than `−4` (like ` −5` or ` −10`) and some more than `−4` (like ` −2` or `8`) in your calculator.
Learner
learner.com › blog › how-to-find-the-range-in-math
How to Find the Range in Math
May 16, 2025 - Subtract the least number in the set from the highest. In the above example, the least number is 1, and the highest is 8. Therefore, the range is 8 -1 =7 · The two main factors of a function are the domain and the range.
Mathematics LibreTexts
math.libretexts.org › bookshelves › applied mathematics › calculus for business and social sciences corequisite workbook (dominguez, martinez, and saykali) › 4: functions
4.7: Domain and Range of a Function - Mathematics LibreTexts
July 18, 2022 - Any value can be chosen for \(z\), so the domain of the function is all real numbers, or as written in interval notation, is: \(D:(−\infty , \infty )\) To find the range, examine inside the absolute value symbols.
Leeversfoods
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shop.leeversfoods.com - How To Calculate Range Of A Function
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Wikihow
wikihow.com › education and communications › studying › mathematics › how to find the range of a function: tutorial + examples
How to Find the Range of a Function: Tutorial + Examples
May 19, 2024 - This refers to the Arithmetic Mean ... GM. In some cases, this can be used to find upper or lower bounds for the range of a function. For example, find the range of f(x) = x^2 + 1/x^2. It obviously has a minimum, but where? Many calculus students will immediately take a ...
Unacademy
unacademy.com › cbse class 11 › cbse class 11 study materials › mathematics › the range of a function
WHAT IS THE RANGE OF A FUNCTION?
March 21, 2022 - Ans – To calculate the range of a function using the graphical method, first, draw the graph of the function and then note down the minimum and maximum value of y on the y- axis over which the graph is spread.