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- 3.2: Domain and Range
- Domain, Range and Codomain
- Domain and Range of Rational Functions
- 3.2: Domain and Range

## 3.2: Domain and Range

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, Range and Codomain

The domain of a rational function consists of all the real numbers x except those for which the denominator is 0. To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x. One way of finding the range of a rational function is by finding the domain of the inverse function. The graph approaches x -axis as x tends to positive or negative infinity, but never touches the x -axis. That is, the function can take all the real values except 0. So, the range of the function is the set of real numbers except 0.

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. Determine the domain and range in each of the relations presented in these relation mapping worksheets for grade 8 and high school students. Observe each relation and write the domain x and range y values in set notation.

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 of.

## Domain and Range of Rational Functions

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. In this section, we will investigate methods for determining the domain and range of functions such as these. In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions.

Solution There are no restrictions on the domain, as any real number may be cubed and then subtracted from the result. Then sketch the graph. Introduction 2 2. Which of the following graphs represent functions? For many functions, the domain and range can be determined from a graph.

*Graph the function on a coordinate plane. Remember that when no base is shown, the base is understood to be *

### 3.2: Domain and Range

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?

Domain refers to: Range refers to: Domain and range can be written in multiple ways: 1. Worked example: domain and range from graph Our mission is to provide a free, world-class education to anyone, anywhere. Using the tree table above, determine a reasonable domain and range. You need each room for two nights. The range of a function is the set of values that the function assumes.

You may also be interested in some of my foldable bundles: The domain is the set of possible input values, or the time t. Some of the worksheets for this concept are Discrete and continuous domains, Discrete continuous, Name class date 2 6, Discrete math i practice problems for exam ii, Objective define the domain and range of discrete and, Discrete math i work 5 , Continuity date period, Sets and set operations. Discrete Functions - Displaying top 8 worksheets found for this concept. These pages are perfect for homework, independent practice, and review. That is why, when we do something with discrete and continuous data, actually we do something with numerical data. These tests have many u, This is a great activity to have students interacting cooperatively and reteaching concepts to one another.

#### Input and Output

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 In fact the Domain is an essential part of the function. Change the Domain and we have a different function.

The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

- Когда эти стены рухнут, вся планета получит высший уровень допуска к нашим секретам. Высший уровень. К отчетам о секретных операциях. К зарубежной агентурной сети. Им станут известны имена и местонахождение всех лиц, проходящих по федеральной программе защиты свидетелей, коды запуска межконтинентальных ракет.

Он распорядился установить жучок в личном компьютере Стратмора - чтобы контролировать его электронную почту, его внутриведомственную переписку, а также мозговые штурмы, которые тот время от времени предпринимал. Если Стратмор окажется на грани срыва, директор заметит первые симптомы. Но вместо признаков срыва Фонтейн обнаружил подготовительную работу над беспрецедентной разведывательной операцией, которую только можно было себе представить. Неудивительно, что Стратмор просиживает штаны на работе.

Последние слова предсмертной записки Хейла крутились у нее в голове, не повинуясь никаким приказам. И в первую очередь я искренне сожалею о Дэвиде Беккере. Простите .

*В действительности перехват электронных писем, передвигаемых по Интернету, был детской забавой для технических гуру из АНБ. Интернет не был создан, как считали многие, в эру домашних персональных компьютеров.*