Can someone please explain range and domain to me?

Question

I've had a few people try to explain it to me but I just don't understand it. Please explain it to me like I am a 5 year old. I think that's the only way I am going to get it. Thanks...

Answer 1

It is very very simple, and try not to think much of it, but....



Domain are all numbers that are x values

&

Range are all numbers that are y values



So say you have a dot on a graph at (1,2)



The 1 is the x part of the dot so it is the domain part.

The 2 is the y part of the dot so it is the range part.



Later on you can apply this simple idea to explain how certain types of lines act.

Answer 2

Domain:



Domain is, by definition, the set of all abscissa (the variable x when working with the coordinate plane) that are allowed to be inputted into the equation. Of course, that is probably not easily understood, so here is a way to think of it: x what you put into that equation, and the domain states what x can be. If x were all of your shirts, but you only wanted to wear white ones, the white shirts would be your domain. You would not consider the other shirts. Mathematically, the domain can be limited to all positive numbers, all integers, or any numbers in between 1 and 3. These are the only value that can be put into your equation. When finding domain, look for two key things, dividing by zero and taking the even (square) root of a negative number. (If you have learned logarithms, add a third: taking the log of a negative number or 0). If an x value will cause you to do any of those forbidden operations, it is not in the domain. For instance, the equation 1/x. The domain cannot include 0, because that would cause dividing by zero. Another example: sqrt(x). The domain cannot include negative numbers, because you cannot take the square root of a negative number. So the domain is all positive numbers. Getting more complicated, try 1/(x-2). x is allowed to be zero, because that would result in 1/(0-2) = -1/2. However, the entire denominator cannot equal zero, so x-2 != 0, x != 2 (!= means not equal to). The domain is all numbers except for 2. Try another, sqrt(x-2). 2 would cause the square root of 0, which is allowed, but any number less than two would result in the square root of a negative. Therefore, the domain is any number 2 or greater. One more thing to remember, all factors must be taken into account because they must all be checked when they equal 0. Take 1/(x-2)(x-3). x cannot be 3 or 2 because they both cause the denominator to be zero. When dealing with square roots, it is more complicated, just remember that an even number of negatives is ok, but an odd number of negatives is not, because that results in the square root of a negative.



Range:



Range is the set of all ordinates (y values in a coordinate plane) that are possible for the equation. The domain is what you put in, the range is what comes out. Let's say the domain are the chemicals H and O. The range is all the possible outcomes. Therefore, the range includes O2 (oxygen), H2O (water), OH (hydroxic acid), etc. However the range does not include NH3 because N was not part of the domain. It is not a possible output. There are many kinds of equations with different ranges and you will learn them with experience, but here are a few. 1/x, the domain is all numbers except for 0, and the range is all numbers except 0, because it can be both positive and negative. Try x=-1, and x=1. However, it will never equal zero because the numerator is a constant. sqrt(x), the domain is all positive numbers, but the range is all numbers because the square root of a number can be both positive and negative. sqrt(4) = 2 and -2. x^2, the domain is all numbers, but the range can only be positive numbers.



A quick note: sometimes the domain will be preset, such as {1,2,3}. To find range, input each into the equation. For instance, in 2x, the range would be {2,4,6}.



I understand this was a long read, but I hope it helps you better understand domain and range. Let me know if this was helpful.

Answer 3

Ok, maybe it's clearer if you think in terms of functions. Functions are like machines or mapping rules which takes inputs (usually x) and spits out an output (y or f(x)). If you graphed your function, the x values are shown on the x-axis and the outputs are shown on the y-axis.



The domain is the set of allowable inputs you're allowed to plug into a function. Depending on the exact function, there are certain values you're not allowed to plug in. For example, you cannot put values of x in which would make the denominator of the function zero. Another one would be square root of negative numbers, or logs of zero and negative numbers.



The range is the resulting set of values which are output. These may be limited both by the nature of the function itself as well as the domain restrictions placed. e.g. for quadratic functions you'll always get a minimum or maximum value, whatever input you put into the function. Or sin and cos which can only range between -1 and 1.



Functions come in all sizes and flavours, so you'll probably need to know some basic properties of different types of functions.

Answer 4

Range-The X intercept of a function on a line. If you are to make a graph and you have the equation y=2x+6 then the range is any value for x when you solve that

Domain-They y intercept of a function one a line. If you are to make a graph and you have the equation y=2x+6 then the range is any value for x when you solve that.



y=2x+6

-6=2x

-3=x



y=2(-3)+6

y=-6+6

y=0



So the range for this problem could be a -3 and the domain is 0. Sorry if this doesn't help at all.

Answer 5

domain is set of all possible values of x for a function

and range is all y values of a function



so domain = from which point to which point the function exist on x axis

and range from which point to which point the function exist on y axis

for most of functions it's all real numbers

Answer 6

domain and range is going to be pretty much ur x and y axis on a graph

domain = x

range = y



so on a graph, if the cordinates are... say (5,6) and (9,6)

then ur domain would be {5,9}

and ur range would be {6,6}

Answer 7

I guess you know what x-coordinates and y-coordinates are.



So, the set of x-coordinates is the domain and the set of y-coordinates is the range.