5. Rational Functions

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)

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. ƒ(x)=(x²-16)/(x+4)

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)

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies directly as x. y = 65 when x = 5. Find y when x = 12.

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.

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

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

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

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 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)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x²+1)/(x²+9)

Provide a short answer to each question. What is the domain of the function ƒ(x)=1/x? What is its range?

Provide a short answer to each question. Is ƒ(x)=1/x² an even or an odd function? What symmetry does its graph exhibit?

Use transformations of f(x)=1/x or f(x)=1/x² to graph each rational function. h(x)=1/x² − 4

Find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=12x/(3x²+1)

Use the graph of the rational function in the figure shown to complete each statement in Exercises 15–20.

As $x\to -2^{+},f\left(x\right)\to$ __