Final answer:
To determine at which numbers a function is not continuous, we need to look for any discontinuities. Discontinuities can occur at points where the function is not defined, or where the graph has a jump, break, or hole.
Step-by-step explanation:
In mathematics, a function is said to be continuous if there are no sudden jumps, breaks, or holes in its graph. To determine at which numbers a function is not continuous, we need to look for any discontinuities. Discontinuities can occur at points where the function is not defined, or where the graph has a jump, break, or hole. These points are often called the points of discontinuity.
For example, consider the function f(x) = 1/x. This function is not defined at x = 0, so there is a discontinuity at that point. Another example is the function f(x) = |x|. This function has a jump at x = 0, where the graph abruptly changes direction.
Therefore, to find the numbers at which a function is not continuous, we need to identify any points where the function is not defined or where there are jumps, breaks, or holes in the graph.