from the graph of f, state each x - value at which f is discontinuous. for each x - value, determine whether…

Explanation:

Step1: Recall continuity definition

A function (y = f(x)) is continuous at (x=a) if (\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)). Discontinuities occur where this fails.

Step2: Examine the graph for breaks

Look for jumps, holes, or vertical - asymptotes in the graph of (y = f(x)).

Step3: Check left - hand and right - hand limits

For each (x) - value of discontinuity, determine if the limit as (x) approaches from the left ((\lim_{x\rightarrow a^{-}}f(x))) or from the right ((\lim_{x\rightarrow a^{+}}f(x))) exists and is equal to the function value at that point (if defined).

Without seeing the actual graph clearly, assume the following general approach for a function with discontinuities at (x = x_1,x_2,x_3,x_4) (in ascending order): If at (x = x_1), the function has a break and (\lim_{x\rightarrow x_1^{+}}f(x)) exists and is equal to (f(x_1)) (if (f(x_1)) is defined in the right - hand sense), then it is continuous from the right. If (\lim_{x\rightarrow x_2^{-}}f(x)) exists and is equal to (f(x_2)) (if (f(x_2)) is defined in the left - hand sense), then it is continuous from the left.

Answer:

Without the actual graph details, we cannot provide specific (x) - values and continuity types. But the process to find the (x) - values of discontinuity and their left/right - hand continuity is as described above. You need to identify the (x) - values where the graph has breaks, jumps, or holes and then check the left - hand and right - hand limits at those points.