Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?
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.
The correct statement is A. f(x) can be odd or even.
The given condition implies that the function is strictly increasing. In other words, for any two values p and q where p < q, f(p) < f(q). This means that the function is not restricted to being odd or even.
An odd function is symmetric about the origin, meaning that f(x) = -f(-x) for all values of x. An even function is symmetric about the y-axis, meaning that f(x) = f(-x) for all values of x.
Since the condition does not give any information about the symmetry of the function, it is possible for f(x) to be odd or even. Therefore, the correct statement is A. f(x) can be odd or even.