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:

Step1: Analyze right end behavior

As $x \to +\infty$, the graph of $f(x)$ moves downward, so $y \to -\infty$.

Step2: Analyze left end behavior

As $x \to -\infty$, the graph of $f(x)$ moves upward, so $y \to +\infty$.

Answer:

as $x \to \infty, y \to -\infty$ and as $x \to -\infty, y \to \infty$