How do convergence of $\lim_{x \to +\infty} |f(x)/g(x)| $ and being less than infinity of that imply and mean that $f(x)$ is upper-bounded by $g(x)$?

Question

I'm trying to learn about asymptotic notation and I have some questions about some paragraphs that I've read.

the Big O. And it's written like this. $f(x) = O(g(x))$.
And it means that the $\lim_{x \to +\infty} |f(x)/g(x)| $ is convergence-- is less than infinity ( $\lim_{x \to +\infty} |f(x)/g(x)| < \infty$ ).
So it's finite, and it can't diverge.

The interpretation is that $f(x)$ function is up to constant factors upper-bounded by $g(x)$, that $f(x)$ grows the same rate or slower than $g(x)$ grows as $x$ gets large.

I have 2 questions from this paragraph.

1. How do convergence of $\lim_{x \to +\infty} |f(x)/g(x)| $ and being less than infinity of that imply and mean that $f(x)$ is upper-bounded by $g(x)$? where does this interpretation come from? I'm trying to somehow imagine their curves but I cant and I have not any clue.

2. in "$f(x)$ function is up to constant factors upper-bounded by $g(x)$", what does up to constant factors mean? I'm not native English speaker and I'm not sure which meanings of "up to" is suitable for this situation and context.

Thanks.