Question

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

Explanation:

To determine the end - behavior of the function \(y = f(x)\) from its graph:

• When we look at the right - hand side of the graph (as \(x\to\infty\)), the graph is moving upwards, which means that as \(x\) approaches positive infinity (\(x\to\infty\)), \(y\) approaches positive infinity (\(y\to\infty\)).
• When we look at the left - hand side of the graph (as \(x\to-\infty\)), the graph is moving downwards, which means that as \(x\) approaches negative infinity (\(x\to-\infty\)), \(y\) approaches negative infinity (\(y\to-\infty\)).

We then match this behavior with the given options. The option that has "as \(x\to\infty,y\to\infty\) and as \(x\to-\infty,y\to-\infty\)" is the correct one.

Answer:

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