Question

the graph of ( y = f(x) ) is graphed below. what is the end behavior of ( f(x) )?
answer
( circ ) as ( x \to -infty ), ( f(x) \to infty ) and
as ( x \to infty ), ( f(x) \to -infty )
( circ ) as ( x \to -infty ), ( f(x) \to -infty ) and
as ( x \to infty ), ( f(x) \to infty )
( circ ) as ( x \to -infty ), ( f(x) \to infty ) and
as ( x \to infty ), ( f(x) \to infty )
( circ ) 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 \( x \to -\infty \) (moving left on the x - axis). The graph is going upwards, so \( f(x)\to\infty \) as \( x\to -\infty \).

Step2: Analyze right end behavior

Look at the graph as \( x \to \infty \) (moving right on the x - axis). The graph is going upwards, so \( f(x)\to\infty \) as \( x\to \infty \).

Answer:

as \( x \to -\infty, f(x) \to \infty \) and as \( x \to \infty, f(x) \to \infty \) (the third option in the list of choices)