Pre-Calc P5 Hw 12.16.24: Rational Functions - Slant Asymptotes

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or intersects.

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one more than the degree of the denominator in a rational function.

Front

How do you find the slant asymptote of a rational function?

Back

To find the slant asymptote, perform polynomial long division on the rational function and take the quotient.

Front

What is the slant asymptote of f(x) = (x^2 - 4x + 2)/(x + 3)?

Back

y = x - 7.

Front

What is the slant asymptote of f(x) = (3x^3 - 2x + 1)/(x^2 + 4x + 2)?

Back

y = 3x - 12.

Front

What is the slant asymptote of f(x) = (x^2 - 2x - 8)/(x - 2)?

Back

y = x.

Front

What is the significance of the slant asymptote in graphing rational functions?

Back

The slant asymptote provides a guide for the end behavior of the graph as x approaches infinity or negative infinity.

Front

What happens to the graph of a rational function as it approaches its slant asymptote?

Back

The graph will get closer to the slant asymptote but will never actually touch it.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.