Determine $$ \lim _{x \rightarrow-1^{-}} f(x) $$ where $$ f(x)=\left\{\begin{array}{ll}-5 & \text { if } x \leq-1 \ 3 x-7 & \text { if }-11\end{array}\right. $$ If the answer in infinity, you can type in INF. If the answer is negative infinity, you can type -INF. If the answer is does not exist, you can type in DNE. Otherwise type in the appropriate number.

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To determine the limit $$ \lim _{x \rightarrow-1^{-}} f(x) $$ for the given piecewise function:

$$
f(x)=\left\{\begin{array}{ll}
-5 & \text{if } x \leq -1 \
3x - 7 & \text{if } -1 < x \leq 1 \
7x^{2} & \text{if } x > 1
\end{array}\right.
$$

we need to consider the behavior of $$ f(x) $$ as $$ x $$ approaches $$-1$$ from the left (i.e., $$ x $$ approaches $$-1$$ with values less than $$-1$$).

For $$ x \leq -1 $$, the function $$ f(x) $$ is defined as a constant value:
$$
f(x) = -5
$$

Since $$ f(x) $$ is constant for all $$ x \leq -1 $$, as $$ x $$ approaches $$-1$$ from the left, the value of $$ f(x) $$ remains $$-5$$.

Therefore, the limit is:

$$
\lim _{x \rightarrow-1^{-}} f(x) = -5
$$

**Answer:** 
-5
The limit is -5.

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