Exploring Rational Functions and Holes

What is the main topic introduced in the first section of the video?

• Polynomial functions

• Rational functions and holes

• Trigonometric functions

• Exponential functions

In the context of rational functions, what does a 'hole' in the graph represent?

• A point where the function intersects the x-axis

• A point where the function has a minimum

• A point where the function has a maximum

• A point where the function is undefined

What is the limit of the function as x approaches 3 from the left in the given example?

• 1

• 2

• 0

• 3

When factoring a rational function, what causes a hole in the graph?

• When the numerator is zero

• When the denominator is zero

• When a factor cancels out in both the numerator and the denominator

• When the function has a vertical asymptote

What is the y-value the function approaches as x approaches -3 from the left in the second example?

• -1

• -2

• 0

• 1

How can you use a table of values to understand the behavior of a function near a hole?

• By finding the maximum value

• By finding the minimum value

• By observing the values as they get closer to the hole

• By calculating the derivative

What happens to the function value as x approaches -3 from the right in the table of values example?

• It approaches -1

• It approaches -2

• It approaches 0

• It approaches 1

In the advanced example, what type of function is left after canceling out the factors?

• Exponential function

• Linear function

• Cubic function

• Quadratic function

What is the horizontal asymptote of the function in the advanced example?

• y = 0

• y = 1

• y = -1

• y = 2

What is the behavior of the function as x approaches negative infinity in the final example?

• It approaches infinity

• It approaches -1

• It approaches 1

• It approaches 0