Question

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

Short answer

The above statement is true.

Step-by-step solution

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.

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.

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.