Understanding Limits and Asymptotes

What is the foundational rational function for understanding horizontal asymptotes?

• x/2

• x^3

• 1/x

• x^2

When the degree of the numerator equals the degree of the denominator in a rational function, what determines the limit?

• The difference between the degrees

• The leading coefficient of the numerator divided by the leading coefficient of the denominator

• The sum of the coefficients

• The product of the coefficients

For a rational function where the degree of the numerator is less than the degree of the denominator, what is the limit as x approaches infinity?

• Undefined

• Zero

• Negative infinity

• Infinity

What happens to the limit of a rational function when the degree of the numerator is greater than the degree of the denominator?

• It approaches zero

• It becomes undefined

• It remains constant

• It approaches either positive or negative infinity

Which technique is used to simplify limits involving radical functions?

• Using derivatives

• Factoring

• Multiplying conjugates

• Completing the square