Question

Question 1: if a function is undefined at a point can that point be its domain. Explain

Question 2: explain what is meant by the minimum value of a function

Answer 1

since a function maps values in its domain to values in the range, if the y-value is undefined, the x-value cannot be in the domain.

Surely the minimum value of a function is the least y-value in the range. For continuous functions, that is no problem. But, if there are point discontinuities, there might be no minimum value. For example, consider the function

y = x^3/x

This is clearly just x^2, but only if x≠0. As written, f(0) does not exist. So, there is no minimum value for y. The limit of y is zero as x->0, but there is no smallest number greater than zero. Whatever value you pick, I can take half of that, and it is less!