Question

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

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)