Exploring Rational Functions and Their End Behavior

The video tutorial covers the concept of end behavior in rational functions, using both numerical and algebraic methods to explore how functions behave as they approach infinity. It explains polynomial dominance and introduces horizontal asymptotes, providing graphical examples for verification. The tutorial concludes with evaluating limits and understanding their significance in determining function behavior.

What happens to the value of a rational function as the denominator becomes infinitely large?

• It approaches infinity.

• It approaches zero.

• It remains constant.

• It becomes undefined.

In the context of end behavior, what does it mean when the highest power in the denominator is greater than the highest power in the numerator?

• The function approaches infinity.

• The function becomes undefined.

• The function approaches zero.

• The function remains constant.

When simplifying a rational function for end behavior, what should you do with the highest power terms?

• Ignore them.

• Focus only on them.

• Multiply them.

• Divide them.

If the degree of the numerator is greater than the degree of the denominator, what is the end behavior of the rational function?

• It remains constant.

• It approaches infinity.

• It approaches zero.

• It oscillates.

In the example where the highest power in the numerator is x^3 and in the denominator is x^2, what is the end behavior?

• It approaches zero.

• It oscillates.

• It approaches infinity.

• It remains constant.

What is the horizontal asymptote of a rational function where the degrees of the numerator and denominator are equal?

• y = 1

• There is no horizontal asymptote

• y = 0

• y = the ratio of the leading coefficients

What happens to the horizontal asymptote if the degree of the denominator is greater than the degree of the numerator?

• It becomes undefined.

• It remains constant.

• It approaches zero.

• It approaches infinity.

What is the limit of a rational function as x approaches infinity if the degrees of the numerator and denominator are the same?

• Infinity

• The ratio of the leading coefficients

• Undefined

• Zero

When evaluating the limit of a rational function as x approaches negative infinity, what should you consider?

• The highest power terms and their coefficients

• The sum of all terms

• The lowest power terms

• Only the constant terms

In the practice problem, what is the limit of the function as x approaches negative infinity if the highest power term in the numerator is x^3 and in the denominator is x^2?

• Zero

• Undefined

• Infinity

• Negative infinity