The function y = x2 – 25 is a polynomial function. Polynomial functions are differentiable everywhere in their domain, which is all real numbers. This means that for the equation y = x2 – 25, it is differentiable at any value of x.
In interval notation, we can express this as:
- (-∞, ∞)
This implies that there are no restrictions on the x values regarding differentiability, and thus the function is smooth and continuous across its entire domain.