How do you find the domain and range of an equation? (Explain in words?)

Question

tkhunny · Answer

Generally, you start with "All Real Numbers" and see if you can rule out anything.

unklerhaukus · Answer

if your function is of the form $y(x)$

then the domain will be all the $x$'s that make sense

and the range will be all the $y$'s that you can get from these $x$'s

alexh107 · Answer

Ah okay, thank you both!

unklerhaukus · Answer

do you have a particular function in mind?

alexh107 · Answer

No, we only have to describe how to do it, but thanks! I just wasn't sure how to put it into words.

unklerhaukus · Answer

Let look at an example.

$y(x) = \sqrt x$

What is the domain of this function?
what values of $x$ will make senses here?

alexh107 · Answer

All positive numbers?

unklerhaukus · Answer

We can take the square root of any non negative number, but we cannot take the square root of negatives.

unklerhaukus · Answer

Yeah exactly!,
the domain of this function is all positive numbers.

alexh107 · Answer

Okay, thank you. That makes sense.

unklerhaukus · Answer

we could write this as   [0, ∞)

unklerhaukus · Answer

Now what is the range?
what values of $y$ can we get, by taking the square root of a positive number?

alexh107 · Answer

All positive numbers?

unklerhaukus · Answer

Yes!

alexh107 · Answer

Ah okay, I think I get it. Thank you for all your help!

unklerhaukus · Answer

good work!