"Rational functions"
Find the domain and x-intercepts for a rational function:
f(x)= =
since d(3)=0 and d(-3)=0 ,the domain is {(-?,-3) ?)}
2(x-2)(x+1)=0, since n(2)=0 and n(-1)=0 ,the graph of f crosses the x-axis at x=2 and x=-1.
*To find vertical asymptote: y=f(x)
the value of x that makes the function undefined ? x=a
for the function f= where n(x)&d(x) are polynomials .if a is a real number such that d(a)=0and n(a)?0 then the line x=a is a vertical asymptote of the graph of y=f(x).
*To find horizontal asymptote:
a. degree of numerator less than degree of denominator as f(x)=
divide each term in numerator and denominator by the highest power of x as x
f(x)= = ; y=0 the horizontal asymptote.
b. degree of numerator equal to the degree of denominator as