5. Rational Functions

Find the domain of the rational function. Then, write it in lowest terms.

$f\left(x\right)=\frac{x^2+9}{x-3}$

Find the domain of the rational function. Then, write it in lowest terms.

$f\left(x\right)=\frac{6x^5}{2x^2-8}$

In Exercises 1–8, find the domain of each rational function. f(x)=(x+7)/(x²+49)

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=x/(x+4)

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. r(x)=(x²+4x−21)/(x+7)

In Exercises 37–44, find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=12x/(3x²+1)

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x² to graph each rational function. h(x)=1/x² − 4

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(3x²+x−4)/(2x²−5x)

In Exercises 95–98, use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x) = (2x+7)/(x+3)