Question

1. consider the function shown in the graph below.

what is the end behavior of this function?
select the two correct options.
as ( x
ightarrow-infty,f(x)
ightarrowinfty ) as ( x
ightarrowinfty,f(x)
ightarrowinfty )
as ( x
ightarrow-infty,f(x)
ightarrow0 ) as ( x
ightarrowinfty,f(x)
ightarrow0 )
as ( x
ightarrow-infty,f(x)
ightarrow-infty ) as ( x
ightarrowinfty,f(x)
ightarrow-infty )

Explanation:

Step1: Analyze the left - hand end behavior

As \(x\) approaches \(-\infty\), observe the graph. The function values are going downwards. So, as \(x\to-\infty\), \(f(x)\to-\infty\).

Step2: Analyze the right - hand end behavior

As \(x\) approaches \(\infty\), observe the graph. The function values are going downwards. So, as \(x\to\infty\), \(f(x)\to-\infty\).

Answer:

As \(x\to-\infty,f(x)\to-\infty\) and As \(x\to\infty,f(x)\to-\infty\) (i.e., the fifth and sixth options).