Graphing Rational expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

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

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, the asymptote is y=0. If they are equal, divide the leading coefficients.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at values of x that make both the numerator and denominator zero.

Front

How do you condense logarithmic expressions?

Back

Use the properties of logarithms: \( \log_b(m) + \log_b(n) = \log_b(mn) \) and \( \log_b(m) - \log_b(n) = \log_b(\frac{m}{n}) \).

Front

What is the vertical asymptote of a rational function?

Back

The vertical asymptote occurs at values of x that make the denominator zero, provided the numerator is not also zero at that value.

Front

What is the domain of a rational function?

Back

The domain consists of all real numbers except those that make the denominator zero.

Front

How do you simplify a rational expression?

Back

Factor both the numerator and denominator and then cancel any common factors.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity (hole) occurs when a factor cancels out, while a non-removable discontinuity (vertical asymptote) occurs when the factor does not cancel.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the graph of the rational function.

Front

How do you graph a rational function?

Back

Identify asymptotes, intercepts, and test points to determine the shape of the graph.