Question

module 4 quiz (l16 - 20)
100 points possible answered: 7/15
question 8
end behavior of a power function
identify the end behaviors for the function graphed to the right
right hand end behavior:
as ( x \to square ), ( f(x) \to square )
left hand end behavior:
as ( x \to square ), ( f(x) \to square )

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Explanation:

Step1: Analyze right - hand end behavior

As \(x\) approaches \(+\infty\) (right - hand side), looking at the graph, as \(x\) gets larger and larger in the positive direction, the function values \(f(x)\) get more and more negative. So \(f(x)\to-\infty\).

Step2: Analyze left - hand end behavior

As \(x\) approaches \(-\infty\) (left - hand side), looking at the graph, as \(x\) gets larger and larger in the negative direction, the function values \(f(x)\) get more and more positive. So \(f(x)\to+\infty\).

Answer:

Right - hand end behavior: As \(x\to+\infty\), \(f(x)\to-\infty\)
Left - hand end behavior: As \(x\to-\infty\), \(f(x)\to+\infty\)