the graph of $y = f(x)$ has the following features:\n• $f(1)=2$\n• $lim_{x\\to1^{-}}f(x)= - 1$\n•…

the graph of $y = f(x)$ has the following features:\n• $f(1)=2$\n• $lim_{x\\to1^{-}}f(x)= - 1$\n• $lim_{x\\to1^{+}}f(x)= - 1$\nwhich of the following might be a graph of $y = f(x)$?

the graph of $y = f(x)$ has the following features:\n• $f(1)=2$\n• $lim_{x\\to1^{-}}f(x)= - 1$\n• $lim_{x\\to1^{+}}f(x)= - 1$\nwhich of the following might be a graph of $y = f(x)$?

Answer

Explanation:

Step1: Analyze given - function values

We know that $f(1)=2$, so the graph should have a solid - point at $(1,2)$. Also, $\lim_{x\rightarrow1^{-}}f(x)=\lim_{x\rightarrow1^{+}}f(x)= - 1$, which means the left - hand limit and the right - hand limit as $x$ approaches $1$ are both $-1$. This implies that the function has a hole or a break at $y = - 1$ as $x$ approaches $1$.

Step2: Check each graph option

We look for a graph that has a solid point at $(1,2)$ and the function approaching $y=-1$ as $x$ approaches $1$ from both the left and the right.

Answer:

The graph that has a solid point at the coordinates $(1,2)$ and the curve approaching $y = - 1$ as $x$ approaches $1$ from both the left - hand side and the right - hand side. (Since no specific graph options are labeled, we can't point to a particular lettered option, but the description above is the characteristic of the correct graph).