Question

Can someone please explain domain and range to me. In my textbook it says use the graphs to determine the domain and range of the function but im not sure how to.

Answer 1

@Salivanth .. are you just typing a lot?

Answer 2

The domain of the function is all the numbers that you can put into the function, i.e, all possible inputs of the function.

The range of the function is all the numbers you can get out of the function, i.e, all possible outputs of the function.

Let's say we have the following function:

1 = 1
2 = 2
3 = 4

There are three possible inputs for this function; 1, 2, and 3. This is our domain. The domain is every number that can possibly go into our function, and only 1, 2, and 3 can do this.

There are three possible outputs for the function as well, 1, 2, and 4. This is the range. The range is any number that our function can output.

Now that we know what the domain and range are, we need to figure out how to get them off a graph.

When I graph a function, here's what I do. Let's say I need to graph the function:

1 = 3.

What I'll do is, I'll draw a point at (1,3) on the graph. x is our input, 1. y is our output, 3.

If I had to graph the function:

1 = 3
2 = 4
3 = 5

Here's what I'd draw:



Here, our domain is 1 to 3, and our range is 3 to 5. Notice that each input to output has a co-ordinate on the graph. 1 = 3 is (1,3). 2 = 4 is (2,4). 3 = 5 is (3, 5).

So that means that the domain is all the x-values on our graph. The X's on the graph I drew go from 1 to 3...exactly the same as our domain of 1,2,3. This isn't a co-incidence. Every input corresponds to an X-coordinate on our graph.

Similarly, the range is all the y-values on our graph. Each output corresponds to a Y-coordinate on our graph. Our Y starts at 3, and ends at 5 on our graph, and 3, 4, 5 is the range of our function!

So to sum up, to find the domain of a graphed function, use the x-coordinates. To find the range, use the y-coordinates. If the x-coordinates go from -2 to 6, the domain will be -2 to 6. If the range goes from -1 to 5, the range will be -1 to 5.

I'm not really good with explanations, so I've tried to provide as much detail as possible. I hope it helps.