Question

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

Explanation:

Step1: Analyze right end behavior

Look at the graph as \( x \to \infty \) (right end). The graph's rightmost part is rising upwards, so \( y \to \infty \).

Step2: Analyze left end behavior

Look at the graph as \( x \to -\infty \) (left end). The graph's leftmost part is also rising upwards, so \( y \to \infty \).

Answer:

as \( x \to \infty \), \( y \to \infty \) and as \( x \to -\infty \), \( y \to \infty \) (the second option among the choices)