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Graph the function on a coordinate plane. Remember that when no base is shown, the base is understood to be Domain and Range of a Function.

## What is the range of a function?

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math Algebra 1 Functions Introduction to the domain and range of a function.

Intervals and interval notation. What is the domain of a function? What is the range of a function? Worked example: domain and range from graph.

Practice: Domain and range from graph. Next lesson. Current timeTotal duration Math: HSF. Google Classroom Facebook Twitter. Video transcript - As a little bit of a review, we know that if we have some function, let's call it "f".

We don't have to call it "f", but "f" is the letter most typically used for functions, that if I give it an input, a valid input, if I give it a valid input, and I use the variable "x" for that valid input, it is going to map that to an output. It is going to map that, or produce, given this x, it's going to product an output that we would call "f x. A domain is the set of all of the inputs over which the function is defined. So if this the domain here, if this is the domain here, and I take a value here, and I put that in for x, then the function is going to output an f x.

If I take something that's outside of the domain, let me do that in a different color If I take something that is outside of the domain and try to input it into this function, the function will say, "hey, wait wait," "I'm not defined for that thing" "that's outside of the domain. And we have a name for that. That is called the range of the function.

So the range. The range, and the most typical, there's actually a couple of definitions for range, but the most typical definition for range is "the set of all possible outputs. So this right over here is the set of all possible, all possible outputs. All possible outputs. So let's make that a little bit more concrete, with an example.

So let's say that I have the function f x defined as, so once again, I'm gonna input x's, and I have my function f, and I'm gonna output f x. And let's say this def The function definition here, the thing that tries to figure out, "okay, given an x, what f x do I produce? The domain is the set of all valid inputs. So what are the valid inputs here? Well, I could take any real number and input into this, and I could take any real number and I can square it, there's nothing wrong with that, and so the domain is all real numbers.

All, all real, all real numbers. But what's the range? Maybe I'll do that in a different color just to highlight it. What is going to be the range here, what is the set of all possible outputs?

Well if you think about, actually, to help us think about, let me actually draw a graph here. Of what this looks like. What this looks like. So the graph of "f x is equal to x squared" is going to look something like this. So, it's gonna look, it's going to look something like this. I'm obviously hand-drawing it, so it's not perfect.

It's gonna be a parabola with a, with a vertex right here at the origin. So this is the graph, this is the graph, "y is equal to f x ," this of course is the x-axis, this of course is the y-axis. So let's think about it, what is the set of all possible outputs? Well in this case, the set of all possible outputs is the set of all possible y's here. Well, we see, y can take on any non-negative value. So the range here is, the range We could, well we could say it a couple of ways, we could say, "f x ", let me write it this way.

Let's do another example of this, just to make it a little bit, just to make it a little bit, a little bit clearer. Let's say that I had, let's say that I had g x , let's say I have g x , I'll do this in white, let's say it's equal to "x squared over x.

Because right over here, we have to, in our domain, x cannot be equal to zero. If x is equal to zero, we get zero over zero, we get indeterminate form.

So in order for this function to be the exact same function, we have to put that, 'cause it's not obvious now from the definition, we have to say, "x cannot be equal to zero. Now these two function definitions are equivalent.

And we could even graph it. We could graph it, it's going to look, I'm gonna do a quick and dirty version of this graph.

It's gonna look something like, this. It's gonna have a slope of one, but it's gonna have a hole right at zero, 'cause it's not defined at zero. So it's gonna look like this. So the domain here, the domain of g is going to be, "x is a member of the real numbers" "such that x does not equal zero," and the range is actually going to be the same thing. The range here is going to be, we could say "f x is a member of the real numbers" "such that f x does not equal zero. So the big takeaway here is the range is all the pos The set of all possible outputs of your function.

The domain is the set of all valid inputs into your function. Up Next.

## Domain and Range Worksheets

The domain of a function f x is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. In grammar school, you probably called the domain the replacement set and the range the solution set. They may also have been called the input and output of the function. D is not in the domain, since the function is not defined for D. You can also talk about the domain of a relation , where one element in the domain may get mapped to more than one element in the range. Here, the relation is given as a set of ordered pairs. Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math Algebra 1 Functions Introduction to the domain and range of a function. Intervals and interval notation. What is the domain of a function?

→ The domain of a function is the set of all the numbers you can substitute into the function (x- values). The range of a function is the set of all the numbers you can get out of the function (y- values).

## Domain and Range

This compilation of domain and range worksheet pdfs provides 8th grade and high school students with ample practice in determining the domain or the set of possible input values x and range, the resultant or output values y using a variety of exercises with ordered pairs presented on graphs and in table format. Find the domain and range of relations from mapping diagrams, from finite and infinite graphs and more. Get started with our free worksheets. State the domain and range of each relation represented as a set of ordered pairs in Part A and ordered pairs on a graph in Part B of these printable worksheets. Write the Domain and Range Relation - Mapping.

Show your work! Adding and Subtracting Fractions Word Problems 1. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Domain and Range How to find the domain and range? Also, for each problem, determine if the relation given represents a function and record your answers in the appropriate spaces provided for each problem.

Domain Range Increasing Decreasing Worksheet Pdf Notice that the graph from Example 1 and this graph increase to the right of the y-axis and decrease to the left. Free Precalculus worksheets created with Infinite Precalculus. At what pop.

### 3.2: Domain and Range

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out. Please read " What is a Function? Example: this tree grows 20 cm every year, so the height of the tree is related to its age using the function h :. Now, what comes out the Range depends on what we put in the Domain

Хотя Стратмор и сожалел о смерти своего молодого сотрудника, он был уверен, что ее можно отнести к числу оправданных потерь. Фил Чатрукьян не оставил ему выбора. Когда запыхавшийся сотрудник лаборатории безопасности завопил о вирусе, Стратмор, столкнувшийся с ним на лестнице служебного помещения, попытался наставить его на путь истинный. Но Чатрукьян отказывался прислушаться к голосу разума. У нас вирус.

How can you find the domain and range of a function? Work with a partner. The table shows the number of adult and child tickets sold for a school concert. Number.

#### Introduction to the domain and range of a function

ГЛАВА 125 - Сколько у нас времени? - крикнул Джабба. Техники в задней части комнаты не откликнулись. Все их внимание было приковано к ВР. Последний щит угрожающе таял. Сьюзан и Соши занялись поисками во Всемирной паутине.

Стратмора торжествовало победу. ТРАНСТЕКСТ себя оправдал. В интересах сохранения в тайне этого успеха коммандер Стратмор немедленно организовал утечку информации о том, что проект завершился полным провалом. Вся деятельность в крыле, где размещалась шифровалка, якобы сводилась к попыткам зализать раны после своего фиаско ценой в два миллиарда долларов. Правду знала только элита АНБ - ТРАНСТЕКСТ взламывал сотни шифров ежедневно. В условиях, когда пользователи были убеждены, что закодированные с помощью компьютера сообщения не поддаются расшифровке - даже усилиями всемогущего АНБ, - секреты потекли рекой.

- Слово разница особенно важно. Главная разница между Хиросимой и Нагасаки. По-видимому, Танкадо считал, что два эти события чем-то различались между. Выражение лица Фонтейна не изменилось.

*Стратмор что-то задумал.*

В голове у Сьюзан беспрестанно крутилась мысль о контактах Танкадо с Хейлом. Кто будет охранять охранников. - подумала. Quis custodiet ipsos custodes. Эти слова буквально преследовали .

*Перед сердечным приступом мистер Танкадо не почувствовал ничего, кроме легкого укола.*

Скажите, что мы сдаемся. Немедленно! - Джабба достал из кармана мобильник. - Давайте мне его номер.

*Она открыла глаза, словно надеясь увидеть его лицо, его лучистые зеленые глаза и задорную улыбку, и вновь перед ней всплыли буквы от А до Z.*

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Domain refers to: Range refers to: Domain and range can be written in multiple ways: 1.

Find a function and its domain based on the equation of a curve. • Define the range of a given function. Functions. This section defines and gives examples.

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.