Rational Functions Chapter 8

Rational Function A function whose equation can be put in the form where P(x) and Q(x) are polynomials and Q(x) is nonzero

Finding the Domain of a Rational Function Domain of a rational function –the set of real numbers except for those numbers which, when substituted for x, give Q(x) =0 Excluded Value –If substituting the number into the expression leads to a division by 0 Simplify a Rational Function First –Completely factor the numerator/denominator

Examples

Vertical Asymptotes and Domains If k is not in the domain of the rational function (g), then x = k may or may not be a vertical asymptote of the graph of (g).

Quotient Function If (f) and (g) are functions, x is in the domain of both functions, and g(x) is nonzero, then we can form a quotient function

Percentage Formula If m items out of n items have a certain attribute, then the percentage p (written p%) of the n items that have the attribute is

Example The U.S. population can be modeled reasonably by the function where U(t) is the population in millions since The number of teens under age 18 who admit to smoking can be represented reasonably by the function where s(x) is the population in millions since 1990

Examples (Cont) P(t) is the percentage of Americans under 18 years old who smoke. Find P(t). Use P(t) to estimate the percentage of the population under 18 who smoked in 2010.

Multiplying Rational Expressions If and are rational expressions where B and D are nonzero, then First, factor the numerator and denominator Multiply Simplify

Dividing Rational Expressions If and are rational expressions where B, C and D are nonzero, then First, write the quotient as a product by taking the reciprocal of the second part Factor the numerator and denominator Multiply Simplify

Example

REMEMBER ORDER OF OPERATIONS

Adding/Subtracting Rational Expressions If and are rational expressions where B are nonzero, then First, if denominators are different, you must find a common denominator Factor the denominator/find a common factor Multiply numerator and denominator of each term by the missing factor of the common factor Add or subtract and simplify

When Subtracting Remember to Distribute the (-1)

REMEMBER ORDER OF OPERATIONS