About this video
The video finds the domain and range of two parent functions from their graphs. For y = |x| the domain is all real numbers and the range is all non-negative reals, [0, infinity). For y = 1/x both the domain and the range are all real numbers except 0.
You'll be able to
- find the domain and range of y = |x| and y = 1/x from their graphs.
- write a domain or range in interval notation, using brackets and parentheses correctly.
- use a union to write a set that leaves out a single value.
Key words
- domain
- The set of all x values you can input into a function and get a valid output.
- range
- The set of all possible output (y) values of a function.
- interval notation
- A way to write a set of numbers using its endpoints, with [ ] to include an endpoint and ( ) to leave it out.
- union
- Joining two sets together, written with the symbol U.
- non-negative
- Zero or positive.
Transcript
- [Instructor] All right, so let's do a couple of examples of trying to figure out the domain and range of a function based on a graph. So here we have the graph of y is equal to the absolute value of x so pause this video and try to figure out the domain and range.
All right, so let's start with the domain. And just as a reminder, this is the set of all of the x values that I can input into this function and get a valid output. Or the set of all the x values for which this function is defined. Well, I can put any real number for x here and take the absolute value there.
So I could say all real numbers, all real numbers. If I wanted to do it as an interval, I could write something like this. I could go from negative infinity all the way to positive infinity. Any of this would imply that, look, I could put any x in here. Now, the range is a different matter.
You can't get out all real numbers from here. You can see that you can go as low as 0 'cause the absolute value of 0 is 0, but everything else is going to be non-negative. So you could really think about this as all non-negative real numbers, all non-negative real numbers.
Or if you wanted to write it like this, you could say, all right, we can include 0 so we could start at 0 and you can go up to positive infinity. And you can never go up to positive infinity. It's unreachable so that's why we don't include it in the set there, and that's why we just have a parentheses.
Now, let's do another example. Let me turn that one off. So here we have the function y is equal to 1 over x. Pause the video again and try to figure out the domain and range. So the domain, what are all of the x values that I can input here? Well, 1 over x is defined for all x's as long as x does not equal 0.
So I could say all real numbers where... all real numbers x where x does not equal 0. I could do it in the interval like, I just did. Or I could say I could go from negative infinity up to 0 and union or add to that the set going from 0 to infinity, I can't include 0 here.
So either of those would work. Now, what about the range? What are all the possible outputs I could get outta this function? All the possible values for y, at least the way that it's defined there? Well, we're gonna have a similar situation. y can take on any value, except it can never quite be equal to 0.
As x gets really, really positive or really, really negative y approaches 0, but it never quite gets there. So it's actually going to be the same thing. So domain is also, well, I could do the same thing. You could go anywhere from negative infinity to 0. The range is the same thing, I should say.
Union, you could go from 0 to positive infinity. You could also say all real numbers where y or where f of x does not equal a 0.
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