Asymptotes and Rational Functions

This video introduces rational functions, explaining their structure as a ratio of polynomials. It covers key concepts such as domain restrictions, roots, discontinuities, and asymptotes. The video also discusses the importance of polynomial degrees in determining horizontal asymptotes. Viewers are encouraged to watch future videos for more examples and detailed explanations.

What is a rational function?

• A ratio of two polynomial functions

• A constant function

• A function with no variables

• A function with only one polynomial

Why are certain input values excluded from the domain of a rational function?

• They make the function linear

• They make the function constant

• They make the denominator zero

• They make the numerator zero

How can you find the roots of a rational function?

• By setting the function to a constant

• By setting the denominator to zero

• By setting the numerator to zero

• By setting both numerator and denominator to zero

What is a discontinuity in a rational function?

• A point where the function is quadratic

• A point where the function is linear

• A point where the function is constant

• A point where the function is undefined

What causes a vertical asymptote in a rational function?

• Both numerator and denominator equal zero

• The denominator equals zero

• The function is constant

• The numerator equals zero

What is a horizontal asymptote?

• A line the function never crosses

• A line the function approaches as x approaches infinity

• A line the function approaches as y approaches zero

• A line the function crosses at x equals zero

Under what condition does a rational function have a horizontal asymptote at y = 0?

• When the degree of the numerator is less than the degree of the denominator

• When the degrees of the numerator and denominator are equal

• When the function is constant

• When the degree of the numerator is greater than the degree of the denominator

What is a slant asymptote?

• A horizontal line the function approaches

• A point the function crosses

• A vertical line the function approaches

• A diagonal line the function approaches

How do you find the horizontal asymptote when the degrees of the numerator and denominator are equal?

• Add the leading coefficients

• Multiply the leading coefficients

• Subtract the leading coefficients

• Divide the leading coefficients

What happens if the numerator's degree is larger than the denominator's degree?

• There is a slant asymptote

• There is no asymptote

• There is a vertical asymptote

• There is a horizontal asymptote