what is the range of y=2x-2?

Question

mathstudent55 · Answer

Do you know what the range of a function is?

anonymous · Answer

I know that the domain is all real numbers and I graphed it out but I am confused on the range I believe that the range is $$1\le x \le -2$$ but im not sure

anonymous · Answer

or is it $$1\le x \le 1$$

mathstudent55 · Answer

You still haven't answered my question.
Do you know what the range of a function is?
I don't mean the range of this function.
In general, what is the range of a function?

anonymous · Answer

oh it is the y value. oops those were supposed to be y's in those equations

mathstudent55 · Answer

The domain of a function is the set of values that can be used for x.
The range of a function is the set of values that can be used for y.
Ok so far?

anonymous · Answer

Yes that is what I meant when I said that range is the y values.

mathstudent55 · Answer

Ok, so you understand the concept. That's good.

For the function y = 2x - 2, is there any number you can't use for x?

mathstudent55 · Answer

Usually, there are restrictions on x values when there is a square root with x inside or x in a denominator. Here, there are no restrictions. x can be any real number. That means the domain is all real numbers.

anonymous · Answer

Yes I understand that part. Now how do I find the range?

mathstudent55 · Answer

Ok, now that you understand that the domain is every real number, think about the range. The range is all the y values. If you substitute x by every real number, then y will also be every real number.

mathstudent55 · Answer

In fact, if you graph this equation, you'll see that it is a straight line that never ends in both directions. Both the x values and y values go one forever. That means both the domain and the range are all real numbers.

anonymous · Answer

Ok so the range is also all real numbers? That makes sense. I originally thought that but for some reason I thought that the range could not be all real numbers.

mathstudent55 · Answer

As you can see in the graph, as the line goes more and more up to the right, the y-coordinates will get higher and higer for ever. As you go more and more down to the left on the line, y-coordinates go lower and lower also forever. The range is all real numbers.
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