91Ó°ÊÓ

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

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{4-2 x}{3 x-1} $$

For the following exercises, find the inverse of the functions. $$ f(x)=\sqrt{6 x-8}+5 $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=2 x^{4}+6 x^{2}-8 $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. $$ x^{3}+3 x^{2}+4 x+12 ; \quad x+3 $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ f(x)=\frac{1}{2} x^{2}+3 x+1 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies jointly as \(x\) and the square root of \(z\) and when \(x=2\) and \(z=25,\) then \(y=100\).

For the following exercises, determine the end behavior of the functions. $$ f(x)=-x^{4} $$

For the following exercises, find the \(x\) - and \(y\) -intercepts for the functions. $$ f(x)=\frac{x+5}{x^{2}+4} $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=x^{3}-3 x^{2}-x+3 $$