5.6 Rational functions  (Page 11/16)

$f\left(x\right)=\frac{x}{2x+1}$

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

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

$f\left(x\right)=\frac{x^2-4x+3}{x^2-4x-5}$

$f\left(x\right)=\frac{2x^2-32}{6x^2+13x-5}$

$f(x)=\frac{24x^2+6x}{2x+1}$

$f(x)=\frac{4x^2-10}{2x-4}$

$f(x)=\frac{81x^2-18}{3x-2}$

$f(x)=\frac{6x^3-5x}{3x^2+4}$

$f(x)=\frac{x^2+5x+4}{x-1}$

The reciprocal function shifted up two units.

The reciprocal function shifted down one unit and left three units.

The reciprocal squared function shifted to the right 2 units.

The reciprocal squared function shifted down 2 units and right 1 unit.

$p\left(x\right)=\frac{2x-3}{x+4}$

$q\left(x\right)=\frac{x-5}{3x-1}$

$s\left(x\right)=\frac{4}{{\left(x-2\right)}^2}$

$r\left(x\right)=\frac{5}{{\left(x+1\right)}^2}$

$f\left(x\right)=\frac{3x^2-14x-5}{3x^2+8x-16}$

$g\left(x\right)=\frac{2x^2+7x-15}{3x^2-14+15}$

$a\left(x\right)=\frac{x^2+2x-3}{x^2-1}$

$b\left(x\right)=\frac{x^2-x-6}{x^2-4}$

$h\left(x\right)=\frac{2x^2+ x-1}{x-4}$

$k\left(x\right)=\frac{2x^2-3x-20}{x-5}$

$w\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)\left(x-5\right)}{{\left(x+2\right)}^2(x-4)}$

$z\left(x\right)=\frac{{\left(x+2\right)}^2\left(x-5\right)}{\left(x-3\right)\left(x+1\right)\left(x+4\right)}$

Vertical asymptotes at $x=5$ and $x=\mathrm{-5},$ x -intercepts at $(2,0)$ and $(\mathrm{-1},0),$ y -intercept at $\left(0,4\right)$

Vertical asymptotes at $x=\mathrm{-4}$ and $x=\mathrm{-1},$ x- intercepts at $\left(1,0\right)$ and $\left(5,0\right),$ y- intercept at $(0,7)$

Vertical asymptotes at $x=\mathrm{-4}$ and $x=\mathrm{-5},$ x -intercepts at $\left(4,0\right)$ and $\left(\mathrm{-6},0\right),$ Horizontal asymptote at $y=7$

Vertical asymptotes at $x=\mathrm{-3}$ and $x=6,$ x -intercepts at $\left(\mathrm{-2},0\right)$ and $\left(1,0\right),$ Horizontal asymptote at $y=\mathrm{-2}$

Vertical asymptote at $x=\mathrm{-1},$ Double zero at $x=2,$ y -intercept at $(0,2)$

Vertical asymptote at $x=3,$ Double zero at $x=1,$ y -intercept at $(0,4)$

$f(x)=\frac{1}{x-2}$

$f(x)=\frac{x}{x-3}$

$f(x)=\frac{2x}{x+4}$

$f(x)=\frac{2x}{{(x-3)}^2}$

$f(x)=\frac{x^2}{x^2+2x+1}$

$f(x)=\frac{2}{x+1}$

$f(x)=\frac{4}{2x-3}$

$f(x)=\frac{2}{\left(x-1\right)\left(x+2\right)}$

$f(x)=\frac{x+2}{\left(x-1\right)\left(x-4\right)}$

$f(x)=\frac{{(x+3)}^2}{{\left(x-1\right)}^2\left(x+1\right)}$

$f(x)=\frac{x^2-4}{x-2}$

$f(x)=\frac{x^3+1}{x+1}$

$f(x)=\frac{x^2+x-6}{x-2}$

$f(x)=\frac{2x^2+5x-3}{x+3}$

$f(x)=\frac{x^3+x^2}{x+1}$

A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 10 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after $t$ minutes.

A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after $t$ minutes.

The concentration $C$ of a drug in a patient’s bloodstream $t$ hours after injection in given by $C(t)=\frac{2t}{3+t^2}.$ What happens to the concentration of the drug as $t$ increases?

The concentration $C$ of a drug in a patient’s bloodstream _$t$ hours after injection is given by $C(t)=\frac{100t}{2t^2+75}.$ Use a calculator to approximate the time when the concentration is highest.

An open box with a square base is to have a volume of 108 cubic inches. Find the dimensions of the box that will have minimum surface area. Let $x$ = length of the side of the base.

A rectangular box with a square base is to have a volume of 20 cubic feet. The material for the base costs 30 cents/ square foot. The material for the sides costs 10 cents/square foot. The material for the top costs 20 cents/square foot. Determine the dimensions that will yield minimum cost. Let $x$ = length of the side of the base.

A right circular cylinder has volume of 100 cubic inches. Find the radius and height that will yield minimum surface area. Let $x$ = radius.

A right circular cylinder with no top has a volume of 50 cubic meters. Find the radius that will yield minimum surface area. Let $x$ = radius.

A right circular cylinder is to have a volume of 40 cubic inches. It costs 4 cents/square inch to construct the top and bottom and 1 cent/square inch to construct the rest of the cylinder. Find the radius to yield minimum cost. Let $x$ = radius.