# college calculus

• Jan 28th 2009, 03:20 PM
asweet1
college calculus
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
• Jan 28th 2009, 05:19 PM
chabmgph
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.