Question

I have an ACT practice guide problem that I need answered and explainedIt has a list of answers to choose from I will list that belowA. 1B. -2C. 4D. The limit does not exist.

Answer 1

The limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a.

The limit of a function F exist if and only if

`\begin{gathered} \lim _(x\rightarrow x^+)f(x)=\lim _(x\rightarrow x^-)f(x) \\ \\ \text{The left-hand limit =The Right-hand Limit} \end{gathered}`

Considering the image given, the limit of the function from the left is from the first graph

`\lim _(x\rightarrow1^-)f(x)=4\Rightarrow\text{ The left hand limit}`

Similarly, the limit of f(x) from the right-hand side is on the second graph

`\lim _(x\rightarrow1^+)f(x)=-2\Rightarrow The\text{ Right -hand limit}`

Since

`\begin{gathered} \text{Left-hand limit}\\e Right\text{ hand imit} \\ 4\\e-2 \end{gathered}`

Therefore

The Limit does not exist (D)