Final answer:
To make a function continuous, we need to ensure that the function does not have any gaps, jumps, or removable discontinuities. To find the value of the constant that makes the function continuous, we need to analyze the function and determine the type of discontinuity it has, if any, and then take the appropriate steps to remove or equalize the discontinuity.
Step-by-step explanation:
To make a function continuous, we need to ensure that the function does not have any gaps, jumps, or removable discontinuities. To find the value of the constant that makes the function continuous, we need to examine the function and determine the behavior at the point where continuity is in question.
If the function has a removable discontinuity, we can make it continuous by removing the discontinuity. If the function has a jump discontinuity, we can make it continuous by ensuring that the left-hand limit and the right-hand limit at the point are equal. If the function has an essential discontinuity, there is no single value of the constant that can make it continuous.
Therefore, to find the value of the constant that makes the function continuous, you need to analyze the function and determine the type of discontinuity it has, if any, and then take the appropriate steps to remove or equalize the discontinuity.