graph f, locate all points of discontinuity, and discuss the behavior of f at these points.\n…

Explanation:

Step1: Check left - hand limit at $x = - 1$

For $x\lt - 1$, $f(x)=-1 + x$. Then $\lim_{x\rightarrow - 1^{-}}f(x)=\lim_{x\rightarrow - 1^{-}}(-1 + x)=-1+( - 1)=-2$.

Step2: Check right - hand limit at $x = - 1$

For $x\geq - 1$, $f(x)=5 - x$. Then $\lim_{x\rightarrow - 1^{+}}f(x)=\lim_{x\rightarrow - 1^{+}}(5 - x)=5-( - 1)=6$.

Step3: Evaluate function at $x=-1$

$f(-1)=5-( - 1)=6$.

Step4: Determine continuity

Since $\lim_{x\rightarrow - 1^{-}}f(x)=-2$, $\lim_{x\rightarrow - 1^{+}}f(x)=6$ and $f(-1) = 6$, the left - hand limit is not equal to the right - hand limit at $x=-1$. So the function is discontinuous at $x = - 1$.

Step5: Analyze the graph

For $y=-1 + x$ when $x\lt - 1$, it is a line with slope $1$ and $y$-intercept $-1$. For $y = 5 - x$ when $x\geq - 1$, it is a line with slope $-1$ and $y$-intercept $5$. The correct graph will have a break at $x=-1$.

Answer:

Locate all points of discontinuity: A. The point(s) of discontinuity is/are $x=-1$. (For the graph part, without seeing the actual graph details in full - resolution, we can't choose from A, B, C, D precisely, but the above analysis helps in identifying the correct graph which should have a break at $x = - 1$)