Help with graphing "continuity from left or right"

Question

Problem (#2 specifically)

Honestly the part I specifically have a problem with is the "f is discontinuous from the right at -5" and the other f is continuous. I sorta get the definitions of being continuous from the left and right but I'm having trouble putting it into the graph.

Here's how far I've gotten

Answer 1

The graph could be a bit more precise but I think your intentions are good.

You've got the limits correct so far, although it's safe to add a bit of a dashed or dotted line connecting the $1$ (on the $y$-axis) to the the "hole" to indicate it's at height $1$ (because it seems to have a lower value now). You could do the same with the dot on $(2,5)$.

The function with your graph is indeed continuous from the right at $-1$, but notice that $f(-1)$ doesn't have to be $1$. The graph has to approach $1$ from the left though (due to the given limit), but $f(-1)$ can have any other value as long as the function is continuous from the right.

For the part at $x=-5$, the function doesn't exist on the left of it (due to the domain beginning at $x=-5$), but the graph has to be discontinuous (from the right) at this point: so approach a certain value for $x \to -5$ but give $f(-5)$ another value than this limiting value (like at $x = 2$).