question\nthe graph of ( y = f(x) ) is graphed below. what is the end behavior of ( f(x) )?\nanswer\n(…

question\nthe graph of ( y = f(x) ) is graphed below. what is the end behavior of ( f(x) )?\nanswer\n( \begin{array} { l } { \text { as } x \rightarrow - infty , f ( x ) \rightarrow infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow - infty } \\ { \text { as } x \rightarrow - infty , f ( x ) \rightarrow - infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow - infty } \\ { \text { as } x \rightarrow - infty , f ( x ) \rightarrow infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow infty } \\ { \text { as } x \rightarrow - infty , f ( x ) \rightarrow - infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow infty } end{array} )

question\nthe graph of ( y = f(x) ) is graphed below. what is the end behavior of ( f(x) )?\nanswer\n( \begin{array} { l } { \text { as } x \rightarrow - infty , f ( x ) \rightarrow infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow - infty } \\ { \text { as } x \rightarrow - infty , f ( x ) \rightarrow - infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow - infty } \\ { \text { as } x \rightarrow - infty , f ( x ) \rightarrow infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow infty } \\ { \text { as } x \rightarrow - infty , f ( x ) \rightarrow - infty \text { and } } \\ { \text { as } x \rightarrow infty , f ( x ) \rightarrow infty } end{array} )

Answer

Explanation:

Step1: Analyze the left - hand end behavior

As (x\to-\infty), looking at the graph, the function (y = f(x)) is going downwards. So (f(x)\to-\infty) as (x\to-\infty).

Step2: Analyze the right - hand end behavior

As (x\to+\infty), looking at the graph, the function (y = f(x)) 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 fourth option in the given answer choices)