Answer:
Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?
( is this the complete question ?)
in this case , you have 4 options :
A.) -f(x) can be odd or even.
B.) -f(x) can be odd but cannot be even.
C.) -f(x) can be even but cannot be odd.
D.) -f(x) cannot be odd or even.
Explanation:
option B is correct.
we are given that for any p<q
f(p)<f(q)
this clearly implies that f is an increasing function.
Now we know that if f is an increasing function then -f is always an decreasing function and vice-versa.
so here -f(x) will be an decreasing function.
Let us consider a example f(x)=x then f(x) is clearly an increasing function.
and -f(x)= -x is an decreasing function. also it is an odd function but not an even function.
so option B holds.