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

from the graph of f, state each x - value at which f is discontinuous. for each x - value, determine whether f is continuous from the right, or from the left, or neither. part 1 of 7 to find the numbers for which f is discontinuous, we look for x - values for which the function is not defined or the left and right limits do not match. starting from the left and moving right, the first x - value for which f(x) is discontinuous is x = . at this point, f(x) is not defined. therefore, at this point f is which of the following. continuous from the right continuous from the left neither

from the graph of f, state each x - value at which f is discontinuous. for each x - value, determine whether f is continuous from the right, or from the left, or neither. part 1 of 7 to find the numbers for which f is discontinuous, we look for x - values for which the function is not defined or the left and right limits do not match. starting from the left and moving right, the first x - value for which f(x) is discontinuous is x = . at this point, f(x) is not defined. therefore, at this point f is which of the following. continuous from the right continuous from the left neither

Answer

Explanation:

Step1: Analyze the graph for discontinuities

We start examining the graph from left - hand side. We look for points where the function has breaks, jumps or is undefined.

Step2: Identify the first discontinuous point

By observing the graph, we can see that the function is not defined at (x=-1). 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)). Since (f(-1)) is not defined, the left - hand and right - hand limits cannot be equal to the function value at that point.

Step3: Determine the continuity from sides

For a function to be continuous from the right at (x = a), (\lim_{x\rightarrow a^{+}}f(x)=f(a)) and for continuity from the left (\lim_{x\rightarrow a^{-}}f(x)=f(a)). Since (f(-1)) is not defined, (f(x)) is neither continuous from the right nor from the left at (x=-1).

Answer:

(x = - 1); neither