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

Explanation:

Step1: Analyze left end behavior

Observe the graph as \( x \to -\infty \). The left - most part of the graph (as \( x \) becomes very negative) is going downwards, so as \( x \to -\infty \), \( y \to -\infty \).

Step2: Analyze right end behavior

Observe the graph as \( x \to \infty \). The right - most part of the graph (as \( x \) becomes very positive) is going upwards, so as \( x \to \infty \), \( y \to \infty \).

Answer:

As \( x \to -\infty \), \( y \to -\infty \) and as \( x \to \infty \), \( y \to \infty \) (the last option among the given choices which should be in the form like "as \( x \to -\infty \), \( y \to -\infty \) and as \( x \to \infty \), \( y \to \infty \)")