Question

Which statement describes the function?

increasing at a constant rate
increasing at a varying rate
decreasing at a constant rate
decreasing at a varying rate

Answer 1

I don't see the function or graph — can you paste the equation, table, or image?

If you want to decide by yourself, use this checklist:

- Increasing vs decreasing:
- If f′(x) > 0 for the interval (or function values rise left→right), the function is increasing.
- If f′(x) < 0 (or values fall left→right), it is decreasing.

- Constant vs varying rate:
- If f′(x) is the same constant everywhere (or the slope between any two points is the same), the rate is constant.
- If f′(x) changes with x (or slopes between points change), the rate is varying.

Quick examples:
- f(x) = 2x → increasing at a constant rate.
- f(x) = x^2 (for x>0) → increasing at a varying rate.
- f(x) = −3x → decreasing at a constant rate.
- f(x) = −x^2 (for x>0) → decreasing at a varying rate.

If you share the specific function/graph/table I’ll pick the correct option.