Question

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 \( x \to -\infty \) (moving left on the x - axis). The left - most part of the graph is going downwards, so as \( x \to -\infty \), \( f(x)\to-\infty \).

Step2: Analyze right end behavior

Look at the graph as \( x \to \infty \) (moving right on the x - axis). The right - most part of the graph is going upwards, 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 third option in the list of choices)