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Chapter 4: Q. 1 (page 244)

In Problems 1, determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not.

f(x)=4x5-3x2+5x-2

Short Answer

Expert verified

The given function is a polynomial function.

The degree of the given function is5.

Step by step solution

01

Given information

The given function is f(x)=4x5-3x2+5x-2.

02

Determine the type of the function

The functionfxis a polynomial function because all the powers of xare non-negative integers.

It has a degree of 5 because the highest power of x is 5 .

03

Write the conclusion

fxis a polynomial function.

It has a degree of 5.

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Most popular questions from this chapter

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=2x5-x4-x2+1

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 5000cubic inches. See the illustration.

Part (a): Express the surface areaS of the box as a function ofx.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

G(x)=x4-1x2-x

Find the domain of the rational function.

G(x)=6x+34-x

In Problems 7-44, follow Steps 1through 7 on page 228to analyze the graph of each function.

G(x)=x3+1x2+2x
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