Final answer:
A function is continuous when it has no jumps, breaks, or holes. The largest set on which a function is continuous depends on the nature of the function, including any points where the function might have discontinuities. This can include undefined values or places where the function jumps from one value to another.
Step-by-step explanation:
A function is continuous when it has no jumps, breaks, or holes. To find the largest set on which the function is continuous, we need to consider any points where the function might have discontinuities. These can occur at points where the function is not defined or where it jumps from one value to another.
For example, if we have a piecewise function with two different equations for different intervals, the largest set on which the function is continuous is the set over which the two equations agree.
Alternatively, if we have a rational function, we need to exclude any values of x that would make the denominator zero, as this would result in undefined function values.