Chapter 6

Chapter 6

1. 6.1 Working with Functions: Algebraic Operations

   • 6.6 Rational Functions
     • a rational function r is a quotient of two polynomials
       • r(x)=p(x)/q(x)
         • if P and Q are both linear functions then the graph of r can be obtained from the graph of f(x)=1/x by shifting, stretching and reflecting
     • a rational function can be expressed in three forms: standard form, factored form and compound fraction form
     • to graph a rational function in which P and Q are polynomials of degree 2 or higher, we first find the following information about the graph: the x and y intercepts, the vertical asymptotes (by finding the zeros of Q) and the horizontal asymptotes( by determining the behavior of y as x approaches ∞
   • functions can be added, subtracted, multiplied or divided for the functions f and g.
     • the sum is the function (f+g)(x) = f(x)+g(x)
     • the difference is the function f-g defined by (f-g)(x) =f(x)-g(x)
     • the product is a function fg defined by (fg)(x)=f(x)*g(x)
     • the quotient is the function f/g defined by (f/g)(x)=f(x)/g(x)