Answered

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Consider the polynomial function h(x) = -2x^5+ 8x^4
2x^2+15.
What is the end behavior of the graph of h ?

Consider The Polynomial Function Hx 2x5 8x4 2x215 What Is The End Behavior Of The Graph Of H class=

Sagot :

Answer: B

Step-by-step explanation:

Applying limits, it is found that the end behavior of the graph is:

B. As [tex]x \rightarrow \infty, h(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, h(x) \rightarrow \infty[/tex].

The function is:

[tex]h(x) = -2x^5 + 8x^4 - 2x^2 + 15[/tex]

To find the end behavior, we apply the limits as x goes to infinity, in which just the term with the highest exponent is considered, hence:

[tex]\lim_{x \rightarrow -\infty} h(x) = \lim_{x \rightarrow -\infty} -2x^{5} = -2(-\infty)^5 = -2(-\infty) = \infty[/tex]

Then, as [tex]x \rightarrow -\infty, h(x) \rightarrow \infty[/tex]

[tex]\lim_{x \rightarrow \infty} h(x) = \lim_{x \rightarrow \infty} -2x^{5} = -2(\infty)^5 = -2(\infty) = -\infty[/tex]

Then, as [tex]x \rightarrow \infty, h(x) \rightarrow -\infty[/tex]

Hence, option B is correct.

A similar problem is given at https://brainly.com/question/24248193

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