91Ó°ÊÓ

For the following exercises, find the inverse of the functions with \(a, b, c\) positive real numbers. $$f(x)=a x^{3}+b$$

For the following exercises, use synthetic division to find the quotient and remainder. $$ \frac{-4 x^{3}-x^{2}-12}{x+4} $$

For the following exercises, use a calculator to find the answer. Graph on the same set of axes \(f(x)=x^{2}, f(x)=x^{2}+2\) and \(f(x)=x^{2}, f(x)=x^{2}+5\) and \(f(x)=x^{2}-3 .\) What appears to be the effect of adding a constant?

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. \(f(x)=x^{3}-2 x^{2}-16 x+32\)

For the following exercises, use the given information to answer the questions. The velocity \(v\) of a falling object varies directly to the time, \(t,\) of the fall. If after 2 seconds, the velocity of the object is 64 feet per second, what is the velocity after 5 seconds?

Graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior. $$f(x)=x(x-3)(x+3)$$

For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at \(x=-4\) and \(x=-1, x\) -intercepts at \((1,0)\) and \((5,0), y\) -intercept at \((0,7)\)

For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior. $$ f(x)=x(x-3)(x+3) $$

For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior. $$ f(x)=x(14-2 x)(10-2 x) $$

For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at \(x=-4\) and \(x=-5, x\) -intercepts at \((4,0)\) and \((-6,0),\) horizontal asymptote at \(y=7\)