Critical Points and Function Behavior

The video tutorial explores the concept of limits, focusing on how functions behave as variables approach specific values, particularly when dealing with denominators that cannot equal zero. It emphasizes the importance of factorization in simplifying expressions to evaluate limits. The tutorial also covers evaluating limits as variables approach infinity, using techniques like dividing by the highest power of x. The video includes practical examples and highlights the significance of understanding asymptotes and intercepts in graphing functions.

What is the main issue when evaluating a function as it approaches a specific point where the denominator becomes zero?

• The function becomes undefined.

• The function becomes infinite.

• The function becomes negative.

• The function becomes zero.

Which factorization technique is used to simplify expressions involving cubes?

• Sum of cubes

• Difference of cubes

• Quadratic factorization

• Difference of squares

What is the mnemonic for remembering the signs in the factorization of a difference of cubes?

• Opposite, Opposite, Always Negative

• Opposite, Same, Always Positive

• Same, Same, Always Negative

• Same, Opposite, Always Positive

How is the axis of symmetry in a quadratic function determined?

• Using the formula -a/2b

• Using the formula a/2b

• Using the formula b/2a

• Using the formula -b/2a

What is the significance of labeling critical points in a function?

• They indicate where the function is undefined.

• They show where the function is continuous.

• They highlight the minimum points of the function.

• They mark the maximum points of the function.

What happens to the terms in a fraction when x approaches infinity?

• They approach infinity.

• They remain constant.

• They approach zero.

• They become negative.

Why is it important to divide each term by the highest power of x when evaluating limits at infinity?

• To find the roots of the expression.

• To simplify the expression.

• To eliminate the x terms.

• To make the expression more complex.

What is the horizontal asymptote of a function when the limit as x approaches infinity is 1/2?

• y = 1/2

• y = 1

• y = 2

• y = 0

What is the y-intercept of a function when all x's are set to zero and the result is 3/6?

• 1/4

• 1/3

• 1/2

• 1

What is the result of dividing a term by infinity?

• It approaches zero.

• It becomes infinite.

• It remains unchanged.

• It becomes negative.