5. Rational Functions

Graph each rational function. See Examples 5–9.

$\text{ƒ}\left(x\right)=\left[\right(x+6\left)\right(x-2\left)\right]/\left[\right(x+3\left)\right(x-4\left)\right]$

Graph each rational function. See Examples 5–9.

$\text{ƒ}\left(x\right)=x/(4-x^2)$

Find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=(−2x+1)/(3x+5)

In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. g(x) = (2x - 4)/(x + 3)

Use transformations of f(x) = (1/x) or f(x) = (1/x²) to graph each rational function. g(x) = 1/(x + 2)² - 1

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. g(x)=(x+3)/x(x+4)

In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. h(x) = (x^2 - 3x - 4)/(x^2 - x -6)

Use transformations of f(x)=1/x or f(x)=1/x² to graph each rational function. h(x)=1/(x−3)²+1

Graph each rational function. ƒ(x)=(6-3x)/(4-x)

Follow the seven steps to graph each rational function. f(x)=2x²/(x²−1)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(2x+6)/(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. h(x)=x/x(x+4)

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+3x+4)/(x-5)

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

Graph each rational function. ƒ(x)=[(x+3)(x-5)]/[(x+1)(x-4)]