Find and classify the discontinuity of the rational function

The video tutorial explains the process of factoring expressions, specifically focusing on the difference of squares. It demonstrates how to factor and simplify expressions, identifying holes and asymptotes in functions. The tutorial emphasizes the importance of recognizing when terms can be divided out, leading to holes, and highlights the conditions for asymptotes. The video concludes with reminders about these concepts, ensuring a clear understanding of the material.

What is the factored form of the expression X^2 - 1?

• (X + 2)(X - 2)

• (X + 1)(X + 1)

• (X - 1)(X - 1)

• (X - 1)(X + 1)

What happens to the expression F(X) = (X - 1)(X + 1) when X - 1 is canceled out?

• It becomes F(X) = 1 / (X - 1)

• It becomes F(X) = X + 1

• It becomes F(X) = 1 / (X + 1)

• It becomes F(X) = X - 1

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

• A point where the function has a minimum value

• A point where the function is undefined due to a canceled factor

• A point where the function has a maximum value

• A point where the function crosses the x-axis

Why can't X equal 1 in the function F(X) = 1 / (X + 1)?

• Because it makes the function zero

• Because it makes the function negative

• Because it creates a vertical asymptote

• Because it creates a hole in the function

Why is X = -1 considered a vertical asymptote in the function F(X) = 1 / (X + 1)?

• Because the function approaches infinity as X approaches -1

• Because the function is negative at X = -1

• Because the function is zero at X = -1

• Because the function is undefined at X = -1