91Ó°ÊÓ

For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. $$f(x)=\frac{3 x^{2}-14 x-5}{3 x^{2}+8 x-16}$$

For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote $$f(x)=\frac{x}{x-3}$$

Find the inverse of the functions. \(f(x)=3-\sqrt[3]{x}\)

Is there a limit to the number of variables that can jointly vary? Explain.

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies directly as the fourth power of \(x\) and when \(x=1, y=6\).

For the following exercises, use Kepler's Law, which states that the square of the time, \(T\) , required for a planet to orbit the Sun varies directly with the cube of the mean distance, \(a\) , that the planet is from the Sun. Using Earth's distance of 150 million kilometers, find the equation relating \(T\) and a.

For the following exercises, use Kepler's Law, which states that the square of the time, \(T\) , required for a planet to orbit the Sun varies directly with the cube of the mean distance, \(a\) , that the planet is from the Sun. Using Earth’s distance of 1 astronomical unit (A.U.), determine the time for Saturn to orbit the Sun if its mean distance is 9.54 A.U.

A rectangular plot of land is to be enclosed by fencing. One side is along a river and so needs no fence. If the total fencing available is 600 meters, find the dimensions of the plot to have maximum area.

An object projected from the ground at a 45 degree angle with initial velocity of 120 feet per second has height, \(h\) in terms of horizontal distance traveled, \(x,\) given by \(h(x)=\frac{-32}{(120)^{2}} x^{2}+x\) . Find the maximum height the object attains.

Solve the following application problem. A rectangular field is to be enclosed by fencing. In addition to the enclosing fence, another fence is to divide the field into two parts, running parallel to two sides. If 1,200 feet of fencing is available, find the maximum area that can be enclosed.