Find the value k that makes the function continuous

The video tutorial explains how to make a graph continuous at a specific point by equating two piecewise functions. The teacher guides students through setting equations equal to each other, solving for the variable K, and graphing the results to ensure continuity. The lesson emphasizes understanding the process of making graphs continuous and solving equations involving fractions.

What is the main goal when trying to make two graphs continuous at a certain point?

• To ensure the graphs have the same Y-intercept

• To make the graphs meet at a specific point

• To ensure the graphs have the same slope

• To make the graphs identical in shape

What is the purpose of setting two equations equal to each other in the context of graph continuity?

• To find the slope of the graphs

• To calculate the area under the graphs

• To determine the Y-intercept

• To ensure the graphs are continuous at a specific X value

At which X value are the graphs set to meet in the example provided?

• X = 2

• X = 1

• X = 0

• X = 3

What is the value of K that ensures the graphs are continuous?

• K = -1/2

• K = 0

• K = 1

• K = -1

Why is the Y-intercept important in achieving continuity between the graphs?

• It is irrelevant to graph continuity

• It affects the curvature of the graphs

• It ensures the graphs have the same height at the meeting point

• It determines the slope of the graphs