Question

question
the graph of $y = f(x)$ is graphed below. what is the end behavior of $f(x)$?

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:

Step1: Analyze left end behavior

Look at the graph as \( x \to -\infty \). The leftmost part of the graph is going up, so as \( x \to -\infty \), \( f(x) \to \infty \).

Step2: Analyze right end behavior

Look at the graph as \( x \to \infty \). The rightmost part of the graph is going down, so as \( x \to \infty \), \( f(x) \to -\infty \).

Answer:

As \( x \to -\infty \), \( f(x) \to \infty \) and as \( x \to \infty \), \( f(x) \to -\infty \) (the option corresponding to this description)