Question

due wednesday by 11:59pm points 100 submitting an external tool select all that apply: as $x\to3^{-}, f(x)\to\infty$ as $x\to3^{+}, f(x)\to\infty$ as $x\to3^{-}, f(x)\to -\infty$ as $x\to3^{+}, f(x)\to -\infty$ as $x\to\infty, f(x)\to -2$ as $x\to\infty, f(x)\to 2$

Explanation:

Step1: Analyze left - hand limit

The notation $x
ightarrow3^{-}$ means $x$ approaches 3 from the left. We need to check the behavior of $f(x)$ as $x$ does this. There is no information indicating $f(x)
ightarrow\infty$ or $f(x)
ightarrow-\infty$ from the left - hand side, so we do not select the first and third options.

Step2: Analyze right - hand limit

The notation $x
ightarrow3^{+}$ means $x$ approaches 3 from the right. Given that the second option is marked as correct, it implies that as $x$ approaches 3 from the right, $f(x)
ightarrow\infty$.

Step3: Analyze limits as $x

ightarrow\infty$
The notations $x
ightarrow\infty$ mean $x$ gets infinitely large. There is no information suggesting that $f(x)
ightarrow - 2$ or $f(x)
ightarrow2$ as $x
ightarrow\infty$, so we do not select the fifth and sixth options. And we also do not select the fourth option since we know $f(x)
ightarrow\infty$ as $x
ightarrow3^{+}$ not $f(x)
ightarrow-\infty$.

Answer:

As $x
ightarrow3^{+},f(x)
ightarrow\infty$