Answer
An absolute minimum at $x=a$ and an absolute maximum at $x=c$ .
Work Step by Step
An absolute minimum at $x=a$ and an absolute maximum at $x=c$. Note that $y=g(x)$ is not continuous but still has extrema. When the hypothesis of Theorem 1 is satisfied then extrema are guaranteed, but when the hypothesis is not satisfied, absolute extrema may or may not occur.