Question

what is the right end behavior of this graph?

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image created for vva via desmos; 2024

\\(x \
ightarrow \infty, f(x) \
ightarrow \infty\\)
\\(x \
ightarrow \infty, f(x) \
ightarrow -\infty\\)
\\(x \
ightarrow -\infty, f(x) \
ightarrow -\infty\\)
\\(x \
ightarrow -\infty, f(x) \
ightarrow \infty\\)

Explanation:

Identify the target behavior

$$ \text{Right end behavior means analyzing } f(x) \text{ as } x \to \infty. $$

Analyze the graph's right side

$$ \text{As } x \text{ increases to the right } (x \to \infty)\text{, the curve points downwards indefinitely, meaning } f(x) \to -\infty. $$

Match with the options

$$ x \to \infty, f(x) \to -\infty $$

Answer:

• (A) \(x

ightarrow \infty, f(x)
ightarrow \infty\)

• **(B) \(x

ightarrow \infty, f(x)
ightarrow -\infty\) (Correct answer)**

• (C) \(x

ightarrow -\infty, f(x)
ightarrow -\infty\)

• (D) \(x

ightarrow -\infty, f(x)
ightarrow \infty\)