Question

G= {(x,y):y=x^3}
What is the domain and range of G?

Answer 1

Domain should be R2, you could put any two values into the function and not break it.

The range should be R1.

Answer 2

Huh?

Answer 3

do the one that looks like {x E R} and {y E R}

Answer 4

yeah?

Answer 5

wait, so fir number 11 its what?

Answer 6

11 is {x E R} and 12 is {y E R}

Answer 7

Ohh okays.

Answer 8

You guys are funny...Pamelaa23 this is how it goes:
y=x^3
Your domain is : x values that are allowed
In other words is there any computation that we will have trouble doing if we plug in a particular number for x? The answer is No. Why? Because we know how to raise any number to the third power we simply multiply it by itself three times.

So your domain is: All real numbers (fancy way of saying any number)
x=(-infinity, infinity)
NOTE: Because we are in the field of real numbers but you don't need to really understand that part because you probably haven't worked with other fields yet)

For range is the values/numbers we get when we plug in all of our x's
Well, we use all the numbers for x, so for y we have
y=(-infinity, infinity)

Let's look at another exercise to understand a little better
Try y=1/x
Your domain is allowed values for x right?
Well we cannot divide by 0 so our x better not ever be 0
1/0 is undefined
So our domain is every real number (or every number since we are assuming we are in the field of real numbers) except for 0.
x=(-infinity,0)U(0,infinity)

Well then that means that y will never be 0.
Look at it this way y=1/x is the same as xy=1 (multiply both sides by x)
that means for all the numbers of x and the numbers for y we plug in we always get 1 (if y were to ever equal 0 then that would mean that x*0=0).
So your range (acceptable values for y is everything except 0
y=(-infinity,0)U(0,infinity)