# Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?

-f(x) can be odd or even.

-f(x) can be odd but cannot be even.

-f(x) can be even but cannot be odd.

-f(x) cannot be odd or even.

**Solution:**

For f(x) is a function

such that if p < q,

f(p) < f(q)

This shows that f is an increasing function

We know that

If f is an increasing function

-f is always a decreasing function

So - f(x) is a decreasing function

For example -

Consider f (x) = x is an increasing function

- f(x) = -x is a decreasing function

It is an odd function and not an even function

**Therefore, the statement - f(x) can be odd but cannot be even best described f(x).**

## Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?

-f(x) can be odd or even.

-f(x) can be odd but cannot be even.

-f(x) can be even but cannot be odd.

-f(x) cannot be odd or even.

**Summary:**

Suppose f(x) is a function such that if p < q, f(p) < f(q). The statement - f(x) can be odd but cannot be even best described f(x).

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