How do I find the domain and range in a function?

Question

I know that they domain is the x and range is the y.

Answer 1

The you're well on your way to finding them already.

The domain is whatever value x can be.

If you look at y = x + 1, the domain is from -infinity to infinity because no matter what you put into x, there will be a y value to come out.

If you look at  y = √(x + 1), the domain is from -1 to infinity because no matter what positive value you put in as well as negative one, you will get an output. However, if you put in a negative number, the y-value becomes undefined

If you look at y = 1/x, the domain is every value except for 0 because every other x-value create a corresponding y-value. If we put 0 into x, our equation becomes undefined due to dividing by 0.

 

Now to look at range.

If you look at y = x + 1, the range is again every possible value. As x goes to either infinity, so too does y.

If you look at y = √(x + 1), the range is from 0 to infinity. Since we cannot have a negative square root, the line ends at 0. Square roots still go on up to infinity because though it grows much slower than the x-value, it never does stop growing.

If you look at y = 1/x, the range is all values except for 0. As the values for x get ever closer to zero, the y-value shoots further and further towards their respective infinities. As x becomes larger, however, the lines approach ever closer to 0, but will never reach a value to zero. 1/9999999999999999999999999999999999999999999 is still not the same as zero.