college calculus

Quote:

Originally Posted by asweet1

Let p(x) be a polynomial function of degree n. Determine if each of the following statements is TRUE or FALSE and justify your answer in writing.
NOTE: If you can find a counterexample, the counterexample is enough to justify saying the statement is FALSE.

(a) The domain of p(x) is all real numbers.

(b) The range of p(x) is all real numbers.

(c) p(x) has exactly n x-intercepts (i.e. exactly n roots)

My answers: Just to let you know we just started this class and the professor has taught us nothing so i have no clue what I am doing.

(a) n has all real numbers
(b) n has all real numbers
(c) x=n and x=p

I believe the question is asking you to have "true" or "false" as an answer for each part. (True if you believe the statement is true, and otherwise)

For example,
(b) False. Here is an example: $y=x^2+2$ is a polynomial of degree 2. However, the range of such function is $y \geq 2$ . Thus the statement is false since you can find a counterexample.