91Ó°ÊÓ

For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. \(f(x)=x^{3}-9 x\), between \(x=-4\) and \(x=-2\)

For the following exercises, use the Rational Zero Theorem to find the real solution(s) to each equation. $$ x^{3}+2 x^{2}-9 x-18=0 $$

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(x^{3}-3 x+2\right) \div(x+2) $$

For the following exercises, find the inverse of the functions. $$ f(x)=\frac{x+3}{x+7} $$

For the following exercises, determine the domain and range of the quadratic function. $$ f(x)=2 x^{2}-4 x+2 $$

For the following exercises, determine the end behavior of the functions. $$ f(x)=(2-x)^{7} $$

For the following exercises, use the given information to find the unknown value. \(y\) varies directly as \(x\). When \(x=3\), then \(y=12\). Find \(y\) wneh \(x=20\).

For the following exercises, find the \(x\) - and \(y\) -intercepts for the functions. $$ f(x)=\frac{94-2 x^{2}}{3 x^{2}-12} $$

For the following exercises, find the intercepts of the functions. $$ f(t)=2(t-1)(t+2)(t-3) $$

For the following exercises, find the inverse of the functions. $$ f(x)=\frac{x-2}{x+7} $$