The video tutorial explains how to determine the value of K that makes two functions continuous at a specific point. It begins with a graphical approach, showing how adding a constant shifts the graph vertically. The tutorial then transitions to an algebraic method, setting the equations equal to find the value of K. The key takeaway is that K equals 3, ensuring continuity at X = 0.

What is the main goal when connecting the two parts of the piecewise function?

• To determine the slope of the line

• To make the function continuous

• To find the value of X

• To make the graph symmetrical

What operation is performed on the quadratic function to make the piecewise function continuous?

• Subtracting 3

• Adding 3

• Multiplying by 3

• Dividing by 3

In the algebraic method, what is the value of X where the two functions are set equal?

• X = 1

• X = 2

• X = 0

• X = -1

What is the algebraic expression for the quadratic function in the problem?

• Y = X + 3

• Y = X^2 + K

• Y = X^2 - 3

• Y = X^2 + 3

What is the value of K that makes the piecewise function continuous?

• K = 2

• K = 3

• K = 4

• K = 1