Question

the graph of ( y = f(x) ) is graphed below. what is the end behavior of ( f(x) )?
answer
( circ ) as ( x \to -infty, y \to infty ) and
as ( x \to infty, y \to -infty )
( circ ) as ( x \to -infty, y \to -infty ) and
as ( x \to infty, y \to -infty )
( circ ) as ( x \to -infty, y \to infty ) and
as ( x \to infty, y \to infty )
( circ ) as ( x \to -infty, y \to -infty ) and
as ( x \to infty, y \to infty )

Explanation:

Step1: Analyze left end behavior

Observe the graph as \( x \to -\infty \) (moving left on the x - axis). The graph is going upwards, so \( y \to \infty \) as \( x \to -\infty \).

Step2: Analyze right end behavior

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

Answer:

as \( x \to -\infty,y \to \infty \) and as \( x \to \infty,y \to \infty \) (the option with this description)