Find the value c that fills in the hole to make the function continuous

The video tutorial explains the parent function X^3 and its S curve graph. It covers transformations, such as shifting the graph, and addresses constraints like X not equaling zero. The concept of graph holes is introduced using a boat analogy, emphasizing the need to 'plug' the hole for continuity. The tutorial then demonstrates solving for a value C that makes the function continuous, using equations and calculations to find the correct output value.

How can you determine the value of C that 'plugs the hole' in the function?

What is the significance of finding the output value when X equals 0 in the given function?