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

As $x \to -\infty$, observe the graph extends upward, so $f(x) \to \infty$.

Step2: Analyze right end behavior

As $x \to \infty$, observe the graph extends upward, so $f(x) \to \infty$.

Answer:

as $x \to -\infty, f(x) \to \infty$ and as $x \to \infty, f(x) \to \infty$