For the Domain Hold a ruler, or some similar object, vertically on the left side of the graph. Now slowly move it to the right and mark down the intervals of x where the ruler would be crossing the graph. In this case, the graph heads to the left forever, so we start by thinking of x as -∞. As we move right, the graph is there until we hit x=-1 where there are those open circles indicating that no point exists there. So our first interval is (-∞, -1). As we continue, the ruler intersects the graph from just beyond -1 until we get to more open circles at x=4. So that interval is (-1, 4). After that the graph continues forever to the right which we write as ∞. So that interval is (4, ∞). Putting them together, we get... (-∞, -1) ∪ (-1, 4) ∪ (4, ∞) So the domain is every value of x from -∞ to ∞ except for -1 and 4. For the Range Do the same thing but in the vertical direction. Start with the ruler held horizontally at the bottom of the graph and move up while keeping track of the intervals of y where the ruler crosses the graph. Answer from Bascna on reddit.com
Lumen Learning
courses.lumenlearning.com › waymakercollegealgebra › chapter › find-domain-and-range-from-a-graph
Determine Domain and Range from a Graph | College Algebra
Given the graph, identify the domain and range using interval notation. ... Yes. For example, the domain and range of the cube root function are both the set of all real numbers. We will now return to our set of toolkit functions to determine the domain and range of each.
Pressbooks
ecampusontario.pressbooks.pub › math3080prep › chapter › 2-4-finding-domain-and-range-from-graphs
2.4 Finding Domain and Range from Graphs – Math 3080 Preparation
February 1, 2022 - Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Videos
Mathematics LibreTexts
math.libretexts.org › bookshelves › algebra › college algebra 1e (openstax) › 3: functions
3.3: Domain and Range - Mathematics LibreTexts
October 6, 2021 - Exclude from the domain any input values that have nonreal (or undefined) number outputs. Use the valid input values to determine the range of the output values. Look at the function graph and table values to confirm the actual function behavior. Finding the Domain and Range Using Toolkit Functions
Cuemath
cuemath.com › calculus › domain-and-range-of-a-function
Domain and Range - From Graph | How to Find Domain and Range of a Function?
From the graph, we can observe that the domain and range of the function are all real numbers except 0. Answer: So, the domain and range of f(x) = 1/x is R - {0} (or) (-∞,0) ∪ (0, ∞). Example 3: Find the domain and range of the function ...
Krista King Math
kristakingmath.com › blog › domain-and-range-from-a-graph
How to get the domain and range from the graph of a function — Krista King Math | Online math help
October 27, 2020 - When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up. Hi! I'm krista. I create online courses to help you rock your math class.
Reddit
reddit.com › r/askmath › can someone write the domain and range of this graph? it’s a bit confusing to me.
r/askmath on Reddit: Can someone write the domain and range of this graph? It’s a bit confusing to me.
December 12, 2022 - Are there any x's that you can't plug in? Subtract these from all the real numbers will give you the domain. ... I have never seen these arrows in a graph, what are they for? I would have said Df is -2, 6 as the end of the arrow seems like a ...
Texas Gateway
texasgateway.org › resource › determining-domain-and-range-linear-functions
Determining the Domain and Range for Linear Functions | Texas Gateway
Given a verbal statement or a graph of a linear function, determine its domain and range. ... To determine the domain of a given situation, identify all possible x-values, or values of the independent variable.
University of Kentucky
ms.uky.edu › ma109 › studentguide › sec-domaingraph.html
Domain from a Graph
Click on "Rain" or "Squish" in the graph below to watch the animation for finding the domain. Notice that the graph always goes towards the \(x\)-axis. So, the parts of the graph below the axis actually go up towards the axis. From the animation, you'll see that the domain of this function is \((-6,-1]\cup[3,7]\text{.}\) If you want to see the animation in a larger window, click here 2 .
Study.com
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Finding Domain & Range from the Graph of a Continuous Function | Algebra | Study.com
Step 1: To find the domain of the function, look at the graph, and determine the largest interval of {eq}x {/eq}-values for which there is a graph above, below, or on the {eq}x {/eq}-axis.
Quora
quora.com › How-do-I-find-the-domain-and-range-of-a-graph
How to find the domain and range of a graph - Quora
Answer (1 of 5): Domain is the x numbers that you can put in the equation that work. And the range is the range of Y values that you can get as a result for putting in any x. Example 1. So a line will usually have any x and any y as a result.
IntMath
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Domain and Range of a Function
Find the domain and range for each of the following. ... We can see that x can take any value in the graph, but the resulting y = f(x) values are greater than or equal to 2. ... It is important to label the axes when sketching graphs. It helps with understanding what the graph represents. We saw how to sketch such graphs in Graph of a Function. ... is not defined for t = -2, as this value would result in division by zero. (There would be a 0 on the bottom of the fraction.)
Scrupp
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Mastering Domain & Range: Find Function Domains from Graphs
Consider the function g(x) = √(x + 3). This function involves a square root, which has restrictions on its input. To find the domain, we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not a real number.
Mashup Math
mashupmath.com › blog › how-to-find-domain-and-range-of-a-graph
How to Find Domain and Range of a Graph (Step-by-Step) — Mashup Math
April 9, 2024 - For our first example, we are given the graph of the function f(x)=x^2 and we are tasked with finding the domain and the range (note that our answers must be in interval notation). Figure 08: Find the domain and range of the graph of y=x^2. Remember that the domain refers to all of the possible x-values, and the range refers to all of the possible y-values. Let’s start with finding the domain of this graph. Notice that the graph is a parabola that extends forever on both the left and right-side of zero.
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CK-12 Foundation
ck12.org › all subjects › cbse math › domain and range of a function › how do you find the domain of a graph function?
Flexi answers - How do you find the domain of a graph function? | CK-12 Foundation
September 11, 2025 - To find the domain of a graph function, follow these steps: Identify the x-values: Look at the graph and determine the range of x-values that the function covers. Check for restrictions: Note any points where the function is undefined, such as holes, vertical asymptotes, or endpoints.
Lumen Learning
courses.lumenlearning.com › ivytech-collegealgebra › chapter › find-domain-and-range-from-graphs
Find domain and range from graphs | College Algebra
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Texas Instruments
education.ti.com › en › customer-support › knowledge-base › ti-nspire-family › product-usage › 33591
Solution 33591: Finding the Domain of a Graph Function Using the Domain Command on the TI-Nspire™ CAS Products.
3) Type in the command "domain" using the keypad 4) Press [(] twice and and input x-5)/(3x-21),x) 5) Press [enter] Please see the TI-Nspire CAS products guidebooks for additional information. ... TrademarksSoftware Data PolicyPrivacy PolicyCookie PolicyTerms of UseTerms of Sale & ServicesSupply Chain Transparency ... TI websites use cookies to optimize site functionality and improve your experience.
Cool Math
coolmath.com › algebra › 15-functions › 06-finding-the-domain-01
Finding the Domain of a Function
OK, so suppose we don't have the graph of a function to look at like in the last section... ... So, we'll just be doing domains on these -- which is really where the action is anyway.
Reddit
reddit.com › r/learnmath › how do you find the domain of a function without graphing it?
r/learnmath on Reddit: How do you find the domain of a function without graphing it?
August 28, 2022 -
I've been looking at all sorts of tutorials and walkthroughs on youtube and math-online, but I really can't get it
Please explain to me like I'm the idiot I am :)
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technically the domain is part of the definition of a function and you can have different domains with the same functional equation for example we can have: f: R- to R with f(x)=1/x and g: R+ to R with g(x)=1/x so if I tell you h(x)=1/x you have no information about the domain however in applied math people usually just use a functional equation to represent a function and implicitely set the domain as the biggest possible subset within the real numbers so in the case of our example the function h can accept any real number except 0, hence its biggest possible domain is R \ {0} such that: h: R \ {0} to R with h(x)=1/x so the general strategy is to look for problematic values that cause division by zero or similar issues (like square root from negative numbers) and to exclude them consider for example: f(x)=sqrt(1-x2 ) in this case the problematic values are all x such that: 1-x2 <0 iff 1 < x2 iff 1 < |x| so the domain of f is all real numbers except those with an absolute values bigger than 1, which means only values between -1 and 1 are allowed: f: [-1, 1] to R, f(x)=sqrt(1-x2 )
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For most polynomials, you determine if there is a point that does not exists. For example, y = x/(x-1), you than see when x =1, you get 1/0 which doesn't exist. For y = tan(x), if you know your trig, this is sin(x)/cos(x), so try to solve for when cosx = 0. When x = pi/2, you get 1/0 again which dies not exist. Over time you will learn the domain of specific functions. For example, y= ln(x), the domain is x >0. This is something you either memorize or once you understand the application of ln(x) you intuitively know the domain.