increasing/decreasing function

[Perlita]

Hello,
I have to solve the following problem:
Given a function f whose domain is [-2,2] such that f(-2)=1 and f(2)=3.
a) Can f be increasing on [-2,2] ? Explain
b) Can f be decreasing on [-2,2]? Explain.
c) Suggest a curve representing the function f , knowing that f is neither increasing nor decreasing on [-2,2].

My answers:
a) yes because -2 < 2 and f(-2) < f(2)
b) No : counter-example: -2 and 2 are both in [-2,2] , -2 < 2 but f(-2) is not < f(2)
c) I drew a curve going from (-2,1) to (-1,-2), then (-1,-2) to (2,3) (so the first part is decresing, the second one is increasing)

May anyone tell me if my answers are correct or not?
HELP me finding the good answers please!!!

 

[Ishuda]

First, a matter of definition [my formal schooling was a long time ago so please forgive me if am being pedantic]: A function f is increasing [decreasing] in an interval if for each pair of points a and b in the interval with b<a, f(b) < f(a) [f(b)>f(a)]. That is, increasing/decreasing doesn't just mean somewhere in the interval but everywhere in the interval.


(a) Correct for reason given. Example y = $\displaystyle 1 + \frac{x + 2}{2}$
(b) Correct for reason given.
(c) Correct.

 

[HallsofIvy]

Some texts books say 'f is increasing' if, for b> a, $\displaystyle f(b)\ge f(a)$ and 'f is strictly increasing' if, for b> a, f(b)> f(a). But others say 'f is nondecreasing' in the first case and 'f is increasing' only for the second. You need to check which your text is using or which your teacher wants you to use.

 

[Perlita]

Thanks a lot HallsofIvy and Ishuda