Given graph, find point $c$ at which $f$ has a jump discontinuity but is right-continuous. Find value of $f(c)$ to make $f$ left‑continuous at $c$.

Question

Question(s)

1. Consider the graph of a function.
   
   
   a. Find the point $c$ at which the function has a jump discontinuity but is right-continuous.
   
   b. What value should be assigned to $f(c)$ to make $f$ left‑continuous at $x=c$?

2. Determine the point at which the function $f(x)=(x−13)^{-1}$ is discontinuous. State the type of discontinuity from options

• both left‑continuous and right‑continuous
• neither left‑continuous nor right‑continuous
• right‑continuous but not left‑continuous
• left‑continuous but not right‑continuous
  
  and whether the function is left‑ or right‑continuous.

My Thought Process

For 1a, at first I entered $c=1$, but it says it was wrong because that was for "left continuous" so I think it is $c=5$ for right discontinuous. Is this correct?

I am kind of confused in 1b, because is it asking for $f(5)$? If so, then I think the answer is $f(c) = 4$, but please correct and explain the right answer if I am wrong.

For 2, Obviously this is an infinite discontinuity at $x=13$, but I'm not sure if infinite discontinuities can be left and right continuous. I think the answer is neither left and right continuous because when graphed, there is a vertical asymptote $x=13$. But is this correct?