Find the value k that make the function continous piecewise function

The video tutorial explains the process of factoring expressions to simplify them, particularly when dealing with holes in graphs. It covers how to identify and simplify these holes, and how to visualize them using a graphing calculator. The tutorial also discusses the implications of plugging values into simplified equations and how this affects the graph, specifically addressing the concept of undefined points and how to resolve them.

Why is factoring important when dealing with complex expressions?

• It increases the number of terms in an expression.

• It is only useful for solving equations.

• It helps in simplifying expressions for easier graphing.

• It makes expressions more difficult to understand.

What does the expression simplify to after factoring?

• X + 7

• X - 7

• X * 7

• X / 7

What is a 'hole' in the context of graphing?

• A point where the graph intersects the y-axis.

• A point where the graph changes direction.

• A point where the graph intersects the x-axis.

• A point on the graph that is undefined.

Why can't you plug in 7 into the original expression?

• It simplifies the expression too much.

• It makes the denominator zero.

• It makes the numerator zero.

• It results in a negative number.

What value of K fills the hole in the graph?

• 0

• 14

• 7

• 21