91Ó°ÊÓ

For the following exercises, use Kepler's Law, which states that 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 the Earth's time of 1 year and mean distance of 93 million miles, find the equation relating \(T\) and \(a\) .

For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on the graph of the inverse with \(y\) -coordinates given. $$f(x)=x^{3}-x-2, y=1,2,3$$

Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm which of those possibilities is the actual combination. \(f(x)=x^{3}-1\)

For the following exercises, graph the polynomial functions. Note \(x\) -and \(y\) -intercepts, multiplicity, and end behavior. $$ m(x)=-2 x(x-1)(x+3) $$

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

Make a table to confirm the end behavior of the function. $$f(x)=-x^{3}$$

For the following exercises, make a table to confirm the end behavior of the function. $$ f(x)=-x^{3} $$

For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one. Factor is \(x^{2}+x+1\)

For the following exercises, make a table to confirm the end behavior of the function. $$ f(x)=x^{4}-5 x^{2} $$

Make a table to confirm the end behavior of the function. $$f(x)=x^{4}-5 x^{2}$$