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Chapter 14: Q. 6 (page 889)

True or False Every polynomial function has a graph that can be traced without lifting pencil from paper.

Short Answer

Expert verified

The above statement is true.

Step by step solution

01

Step. 1 Polynomial function introduction

A polynomial function is a function in which there are only non-negative integral powers of the variable in an equation.

02

Step. 2 Meaning of the sentence given in question.

The question says that graph that can be traced without lifting the pencil from paper means that graph must be continuous, there must not be any break in it which leads to the break of contact of pencil from the paper.

03

Step. 3 Final conclusion

Now if we have a polynomial function then it must be continuous on the entire number line as whatever be the limit we set for the polynomial function, the limit will exist as it does not violate any law of mathematics. That's why all polynomial functions are continuous.

Hence, the given statement is true.

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Most popular questions from this chapter

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�0f(x),f(x)=ex

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�-3f(x),f(x)=2x

In Problems 53-56, use the properties of limits and the facts that

limx鈫�0sinxx=1limx鈫�0cosx-1x=0limx鈫�0sinx=0limx鈫�0cosx=1

limx鈫�0sin2x+sinx(cosx-1)x2

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Findlimx鈫�-6+f(x).

In Problems 7鈥� 42, find each limit algebraically

limx鈫�3(2-5x)
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