Question

using the graph, what is the left end behavior?

\\(x \
ightarrow \infty, f(x) \
ightarrow 0\\)
\\(x \
ightarrow -\infty, f(x) \
ightarrow -\infty\\)
\\(x \
ightarrow -\infty, f(x) \
ightarrow \infty\\)
\\(x \
ightarrow -\infty, f(x) \
ightarrow 0\\)

Explanation:

Identify the target behavior

Using the End Behavior knowledge point

$$ \text{Left end behavior describes } f(x) \text{ as } x \to -\infty. $$

Analyze the graph's left side

Using the Exponential Asymptotes knowledge point

$$ \text{As } x \to -\infty, \text{ the curve approaches the horizontal asymptote } y = 0. $$

Match with the given options

Using the End Behavior knowledge point

$$ x \to -\infty, f(x) \to 0 $$

Answer:

• (A) \(x

ightarrow \infty, f(x)
ightarrow 0\)

• (B) \(x

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

• (C) \(x

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

• **(D) \(x

ightarrow -\infty, f(x)
ightarrow 0\) (Correct answer)**