How to find the value k that can make the piecewise function continous

The video tutorial explains how to determine the value of C that makes a function continuous. It begins by discussing the concept of continuity and domain restrictions. The instructor then demonstrates graphing functions to visualize the problem and find the value of C. The tutorial emphasizes the importance of ensuring the functions share a common point at X=0 for continuity. Finally, it covers algebraic methods to set equations equal and solve for C, reinforcing the graphical approach with mathematical representation.

What is the role of the constant C in the context of function continuity?

• It determines the x-intercept.

• It defines the domain of the function.

• It shifts the graph up or down.

• It changes the slope of the function.

In the graphical approach, what value of C makes the function continuous?

• 0

• -3

• 3

• 1

Why is it important for the functions to share a common point?

• To make the function continuous at that point.

• To ensure they have the same slope.

• To determine the x-intercept.

• To define the domain of the function.

How can you algebraically find the value of C that makes the function continuous?

• By determining the x-intercept.

• By calculating the integral of the function.

• By setting the equations equal to each other at X = 0.

• By finding the derivative of the function.

What does setting the equations equal to each other represent in terms of continuity?

• Ensuring the functions have the same domain.

• Ensuring the functions have the same x-intercept.

• Ensuring the functions have the same y-value at a point.

• Ensuring the functions have the same slope.