1. ## Intervals

Hello,

I just finished watching a short video on youtube explaining the concepts of increasing, decreasing, and constant functions. I understand such concepts now, but what was most notable in the video is when the instructor remarked that intervals are named using the
x-values only? To my knowledge, an interval is a portion of real numbers on the real number line (is that correct?). And so, could you not have a interval with respect to the
y-axis--since it is a real number line?

Thank you

2. ## Re: Intervals

Originally Posted by Bashyboy
the instructor remarked that intervals are named using the x-values only? To my knowledge, an interval is a portion of real numbers on the real number line (is that correct?). And so, could you not have a interval with respect to the y-axis--since it is a real number line?
You realize that we have not seen that clip. So we don't know exactly what the lecturer meant. That said, that basically eight non-degenerate interval types, connected subset of at least two real numbers .
$\displaystyle \begin{array}{*{20}c} {(a,b)} & {(a,b]} & {[a,b)} & {[a,b]} \\ {( - \infty ,b)} & {( - \infty ,b]} & {(a,\infty )} & {[a,\infty )} \\ \end{array}$.
Four are bounded and four are unbounded.

Yes we can have intervals on any number line.

3. ## Re: Intervals

YouTube - &#x202a;Increasing, Decreasing, Constant Part 1 3.3&#x202c;&rlm; here it is and thank you for answering my question

4. ## Re: Intervals

I think she said that the interval is defined ONLY over the x values because she didn't want you to get confused between something like the open interval
(a, b) which can be written as a < x < b, as opposed to a point (a,b) where x = a and y = b in the 2-dimensional rectangular coordinate system.

So for example when she describes the interval (-8, -4) she is referring to the set of x values such that -8 < x < -4 as opposed to the point (x,y) = (-8, -4).

However, intervals do not have to be defined with respect to only x. Intervals can be defined on the y - axis, z- axis or any other axis or coordinate system that you may use.