Question

the graph of $y = f(x)$ is graphed below. what is the end behavior of $f(x)$? graph 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 $x \to -\infty, f(x) \to -\infty$

Explanation:

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

1. As \(x

ightarrow\infty\): We look at the right - hand end of the graph. From the given graph, as \(x\) gets larger and larger (moves to the right), the graph of \(y = f(x)\) is going downwards, which means \(f(x)
ightarrow-\infty\).

1. As \(x

ightarrow-\infty\): We look at the left - hand end of the graph. As \(x\) gets smaller and smaller (moves to the left), the graph of \(y = f(x)\) is also going downwards, which means \(f(x)
ightarrow-\infty\).

Answer:

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