Question

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

Explanation:

Step1: Analyze the right - hand end behavior

As \(x\) approaches \(+\infty\) (moving to the right along the \(x\) - axis), we look at the direction of the graph. The graph of \(y = f(x)\) goes up. So, as \(x\to+\infty\), \(f(x)\to+\infty\).

Step2: Analyze the left - hand end behavior

As \(x\) approaches \(-\infty\) (moving to the left along the \(x\) - axis), the graph of \(y = f(x)\) goes down. 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 second option in the given choices).