Asymptotes of Rational Functions 1/21/2016

Vocab Continuous graph – a graph that has no breaks, jumps, or holes Discontinuous graph – a graph that contains breaks, jumps or holes Point of discontinuity – is the x-coordinate of a point where the graph of a function is not continuous Non-removable discontinuity – a break in the graph of a function where you cannot redefine the function to make the graph continuous Removable discontinuity – a point of discontinuity, a, of a function that you can remove be redefining the function at x=a

Horizontal Asymptote

Vertical Asymptote

Holes

X- and Y- intercepts To find the y-intercept of a rational function all the ‘x’ values must be equal to zero and solve. To find the x-intercepts of a rational function the numerator of the rational function must be set equal to zero and solve for the ‘x’ values MUST SIMPLIFY THE RATIONAL EQUATION FIRST

Steps to finding asymptotes, holes, and intercepts 1.Horizontal Asymptote Compare degree of P(x) and Q(x) 2.Simplify 3.Find holes Factors that canceled 4.x- and y- intercepts y- intercept set all x’s equal to zero x- intercept set numerator equal to zero 5.Vertical asymptote Set denominator equal to zero

EX 1 Find the Holes

Ex 2 Find the V.A

Ex 3 Find the H.A.