Could someone explain to me why the range of the graph is R\(0,5]

Question

I am trying to help my brother with his exam preparations, and we came across this question and found the answer a little confusing. Here is the graph and the range, taken from the answers page of the practice questions.

Shouldn't the correct range be R\[0,10)?

I'm guessing the black dot at $x=5$ means that the function takes the value $y=0$ there. Then $0$ would be in the range, and you should not remove it from $R$. — Pierre-Guy Plamondon, Jun 10 '15 at 12:42
No. The symbols $R\setminus [0,10)$ mean that you remove the interval $[0,10)$, which does contain $0$. The correct range should contain $0$ but not $10$, so you need to remove $10$ but not $0$: you then get $R\setminus (0,10]$. — Pierre-Guy Plamondon, Jun 10 '15 at 12:46
range is entire vertical line/Y-axis minus points between 0 and 5 such that 0 is included in the range and 5 is not included in the range which the book chose to write as R \ (0,5], generally it is written as R~(0,5] — Vikram, Jun 10 '15 at 12:48
@Vikram but the graph resumes at 5,10, not 10,5. It should be R\(0,10] — Prodigga, Jun 10 '15 at 12:50
Someone should answer this so I can mark it as answered and give out them points :) — Prodigga, Jun 10 '15 at 12:53
you can answer your own question, it is encouraged, I will upvote it — Vikram, Jun 10 '15 at 12:56

score 0 · Answer 1 · answered Dec 09 '20 at 05:36

Summarizing the contents of the comments so this question can be removed from the "unanswered" queue:

First of all, the book is wrong. The range of this graph is the entire real line except the region between $y=0$ and $y=10$. Since the function is defined at $y=0$ but not at $y=10$, the range should be $R\setminus(0,10]$ (or, more accurately, $\mathbb{R}\setminus(0,10]$).

Could someone explain to me why the range of the graph is R\(0,5]

1 Answers1