pka disagrees with teaching graphs before limits

[pka]

I can answer stuff about limits based on a graph, but I don’t understand how to think about it within the domain of a piecewise functions

Well I completely disagree that one needs to have a graph to work this question.
$w(x)=\begin{cases}-x^3+1 & x\le 1 \\2|x-1|-2 & 1<x<3\\ (x-5)^2-2 & 3\le x \end{cases}$
Look the right column. We have $(-\infty, 1]\cup(1,3)\cup [3,\infty)=\Re$, the set of real numbers.
That tells us that the set of all real numbers is the domain of $w(x).$
Now we have:
$1)~\mathop {\lim }\limits_{x \to - \infty } w(x) = +\infty$
$2)~\mathop {\lim }\limits_{x \to 1^{{\large\bf-}} } w(x) = 0$
$3)~\mathop {\lim }\limits_{x \to 1^{{\large\bf+}} } w(x) = -2$
$4)~\mathop {\lim }\limits_{x \to 3^{{\large\bf-}} } w(x) = 2$
$5)~\mathop {\lim }\limits_{x \to 3^{{\large\bf+}} } w(x) =2$
$6)~\mathop {\lim }\limits_{x \to \infty } w(x) = +\infty$?
Looking at the above limits, tell us what the range is.

 

[Dr.Peterson]

Well I completely disagree that one needs to have a graph to work this question.

I'm confused. The problem said:



And this is a precalculus problem.

 

[pka]

I'm confused. The problem said:

View attachment 28889

And this is a precalculus problem.

Please don't be confused by my dislikes. Many, many problems state things I dislike and I say so.
In this case, I do not see how one is to graph $w(x)$ without knowing the limits.

 

[mmm4444bot]

Many, many problems state things I dislike and I say so.

We know.

We've also asked you many times to not post so many personal dislikes in students' threads. You're free to express them in your own threads, and the Odds&Ends board is the place for complaining about course material.

I do not see how one is to graph $w(x)$ without knowing the limits.

The standard way (before introducing limits) is to use an open dot when an endpoint is not included in the domain and to use a closed dot when it is.

?