Rational Functions

Warm Up Graph Fill in the Table x y -4 -3 -2 -1 1 2 3 4

Rational Function A rational function is a polynomial divided by a polynomial. So, if p(x) and q(x) are polynomials, then p(x)/q(x) is a rational function – and so is q(x)/p(x). Both are polynomials dividing polynomials. Example:

Since we can’t divide by zero, it’s pretty easy to figure out what values will be restricted from the domain of a rational function. If p(x) = x2 + 3x – 10 and g(x) = 2x2 + x – 3 Find the domain of the following rational functions. 1. 2.

Graphing Rational Functions From the warm up we know that rational functions have: A horizontal asymptote, y = 0 (x-axis). A vertical asymptote, x = 0 (y-axis). The graph is in quadrants I and III. The graph has no x- or y-intecepts. The points (1,1) and (-1,-1) are key points to keep track of.

When graphing transformations the function , think about the locations of the asymptotes and the key points. Example: Graph State the transformations, equations of asymptotes and domain.

Graph the following. State the transformations, equations of asymptotes and domain. 1. 2. 3.

Rational Equations Solve Remember what types of equations we have solved that sometimes end up with extraneous solutions? Check your answer.

Solve the following 1. 2. 3.