This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
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The domain of a function is the set of numbers that can go into a given function. In other words, it is the set of x-values that you can put into any given equation. The set of possible y-values is called the range. If you want to know how to find the domain of a function in a variety of situations, just follow these steps.
Things You Should Know
Learn the definition of the domain. The domain is defined as the set of input values for which the function produces an output value. [1] X Research source In other words, the domain is the full set of x-values that can be plugged into a function to produce a y-value.
Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
Joseph MeyerTo solve an equation for a variable like "x," you need to manipulate the equation to isolate x. Use techniques like the distributive property, combining like terms, factoring, adding or subtracting the same number, and multiplying or dividing by the same non-zero number to isolate "x" and find the answer.
State the domain. Just state the domain based on the type of graph you're working with. If you're uncertain and know the equation of the line, plug the x-coordinates back into the function to check. [10] X Research source
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Write down the relation. A relation is simply a set of ordered pairs. Let's say you're working with the following coordinates: <(1, 3), (2, 4), (5, 7)>
Make sure the relation is a function. For a relation to be a function, every time you put in one numerical x coordinate, you should get the same y coordinate. So, if you put in 3 for x, you should always get 6 for y, and so on. The following relation is not a function because the x coordinate, 1, has two different corresponding values of y, 4 and 5. . [12] X Research source
AdvertisementMario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels.
Associate Professor of Mathematics Expert AnswerIf your function is a fraction, set the denominator equal to 0 and solve. The domain would then be all real numbers except for whatever input makes your denominator equal to 0. For a square root, set whatever is inside the radical to greater than or equal to 0 and solve, since you can’t use any inputs that produce an imaginary number (i.e., the square root of a negative).
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Mario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels.
Associate Professor of Mathematics Expert AnswerYes. You can use a graphing calculator to calculate domain by plotting the function. There are also a variety of domain and range calculators online. Simply input your function to find the domain, which is a set of x-values that will successfully generate y-values.
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The function tan(90x/2) is undefined at 90x/2 = pi/2 + pi*n, where n is an integer. Simply solve for x to obtain pi/90 + pi*n/45, where n is an integer.
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This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 2,447,726 times.
56 votes - 63% Co-authors: 45 Updated: July 18, 2024 Views: 2,447,726 Categories: MathematicsIn mathematics, the domain of a function refers to the set of all possible numbers that you can use as inputs, or x-values, in the function. For example, if your function is f(x) = 2x+3, then the domain is any number that you can use in place of x. In this example, and with many other functions, the domain includes all real numbers. However, there are special cases where the domain will be more limited. For instance, if the function includes a fraction with a variable in the denominator, you’ll need to exclude any numbers from your domain that would result in the denominator of the fraction being equal to 0. To figure this out, set the denominator as an equation equal to 0 and solve for x. Let’s say you have a function f(x) = 2x/x^2-4. Start by writing out x^2-4 = 0. Factor the expression to get (x – 2) (x + 2) = 0. When you solve for 0, you’ll get two possible inputs: 2 and -2. This means you must exclude 2 and -2 from the domain. Define the domain as “x = all real numbers except for 2 and -2.” You could also write it as D = (-∞, -2) U (2, ∞). Functions that include natural logs and square roots also require special care when defining the domain. For instance, if the variable is under a square root, you must exclude any values that would result in a negative number under the root sign. The same goes for functions with a natural log. For example, if your function is either f(x) = ln(x – 8) or f(x) = √(x – 8), you’d define the domain as any real number greater than or equal to 8. Another way to write this out is D = [8, ∞). In many cases you can also define the domain of a function by looking at a graph. Look at which values are represented or excluded on the x-axis to help you find the domain. For example, if you’re looking at a graph of a line or a parabola, the domain would be all real numbers, since the graph continues infinitely in both directions. On the other hand, a function with a vertical asymptote at x = 3 would have a domain of all real numbers except for 3. If you want to learn how to find the domain of a function on a coordinate plane, keep reading the article!
