Calculus: True or false statements
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) p(x) has a y intercept.
(b) If n is odd then p(x) has at least one x-intercept
(c) If n is 2, then p (x) is always concave up.
(d) p(x) is continuous at all real numbers (i.e. on the interval (negative infinity, positive infinity)
My teacher has not taught us anything so I am completely lost. However I did try to figure and this is how far I got:
(a) y= x^2+2
(b) Im not sure of this one but i think there is at leats one x intecerpt
(c) He didn't teach us concave. Other than it is like water. Meaning it is either low or high and overflowing
(d)Wouldn't this depend on where the equation starts? Like if it starts in positive infinity it was only be positive infinity