Question

the graph of $y = f(x)$ is graphed below. what is the end behavior of $f(x)$?
graph of a polynomial function with arrows pointing down as $x$ approaches negative and positive infinity
answer

• as $x \to -\infty$, $f(x) \to \infty$ and as $x \to \infty$, $f(x) \to -\infty$
• as $x \to -\infty$, $f(x) \to -\infty$ and as $x \to \infty$, $f(x) \to \infty$
• as $x \to -\infty$, $f(x) \to -\infty$ and as $x \to \infty$, $f(x) \to -\infty$
• as $x \to -\infty$, $f(x) \to \infty$ and as $x \to \infty$, $f(x) \to \infty$

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Explanation:

To determine the end - behavior of the function \(y = f(x)\) from its graph, we look at the direction of the graph as \(x\) approaches positive infinity (\(x
ightarrow\infty\)) and negative infinity (\(x
ightarrow-\infty\)).

• For \(x

ightarrow-\infty\): We observe the left - hand side of the graph. As \(x\) gets more and more negative (moves to the left along the \(x\) - axis), the graph of the function is going downwards, which means \(f(x)
ightarrow-\infty\).

• For \(x

ightarrow\infty\): We observe the right - hand side of the graph. As \(x\) gets more and more positive (moves to the right along the \(x\) - axis), the graph of the function is also going downwards, which means \(f(x)
ightarrow-\infty\).

Answer:

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