91Ó°ÊÓ

For the following exercises, use the Rational Zero Theorem to find the real solution(s) to each equation. $$ 2 x^{3}-3 x^{2}-x+1=0 $$

For the following exercises, use the given information to find the unknown value. \(y\) varies inversely with \(x\). When \(x=3\), then \(y=2\). Find \(y\) when \(x=1\).

For the following exercises, use the vertex \((h, k)\) and a point on the graph \((x, y)\) to find the general form of the equation of the quadratic function. $$ (h, k)=(2,3),(x, y)=(5,12) $$

For the following exercises, find the inverse of the functions. $$ f(x)=x^{2}+4 x+1,[-2, \infty) $$

For the following exercises, describe the local and end behavior of the functions. $$ f(x)=\frac{2 x^{2}-32}{6 x^{2}+13 x-5} $$

For the following exercises, find the intercepts of the functions. $$ f(x)=x\left(x^{2}-2 x-8\right) $$

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.) $$ \left(x^{4}+x^{3}-3 x^{2}-2 x+1\right) \div(x+1) $$

For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. \(f(x)=x^{3}-100 x+2\), between\(x=0.01\) and \(x=0.1\)

For the following exercises, use the Rational Zero Theorem to find the real solution(s) to each equation. $$ 3 x^{3}-x^{2}-11 x-6=0 $$

For the following exercises, use the given information to find the unknown value. \(y\) varies inversely with the square of \(x\). When \(x=4,\) then \(y=3\). Find \(y\) when \(x=2\).