Pre-Calc P1 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 oblique (slant) asymptote?

Back

An oblique asymptote is a line that a graph approaches as x approaches infinity or negative infinity, and it occurs when the degree of the numerator is exactly one more than the degree of the denominator.

Front

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

Back

To find the oblique asymptote, perform polynomial long division on the rational function. The quotient (ignoring the remainder) will give the equation of the oblique asymptote.

Front

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

Back

y = 3x - 12.

Front

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

Back

y = x - 7.

Front

What is the oblique asymptote of (x^2 - 2x - 8) / (x - 2)?

Back

y = x.

Front

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

Back

The graph of the rational function will get closer and closer to the oblique asymptote as x approaches infinity or negative infinity.

Front

What is the degree of a polynomial?

Back

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

Front

If the degree of the numerator is less than the degree of the denominator, what is the horizontal asymptote?

Back

The horizontal asymptote is y = 0.

Front

What is the horizontal asymptote of the function f(x) = (2x^2 + 3) / (4x^2 + 5)?

Back

y = 1/2.