91Ó°ÊÓ

Find the vertical and slant asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph \(f\). $$ f(x)=\frac{x^{2}-2 x-3}{x-1} $$

Proceed as in Example 2 and sketch the graph of the given polynomial function \(f\). \(f(x)=(x+1)(x-2)(x-4)\)

Use synthetic division to find the quotient \(q(x)\) and remainder \(r\) when \(f(x)\) is divided by the given linear polynomial. $$ f(x)=x^{4}+16 ; x-2 $$

Find all real zeros of the given polynomial function \(f\). Then factor \(f(x)\) using only real numbers. $$ f(x)=4 x^{5}-8 x^{4}-24 x^{3}+40 x^{2}-12 x $$

Find all real zeros of the given polynomial function \(f\). Then factor \(f(x)\) using only real numbers. $$ f(x)=6 x^{5}+11 x^{4}-3 x^{3}-2 x^{2} $$

Find the vertical and slant asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph \(f\). $$ f(x)=\frac{-(x-1)^{2}}{x+2} $$

Use synthetic division to find the quotient \(q(x)\) and remainder \(r\) when \(f(x)\) is divided by the given linear polynomial. $$ f(x)=4 x^{4}+3 x^{3}-x^{2}-5 x-6 ; x+3 $$

Find a polynomial function \(f\) with real coefficients of the indicated degree that possesses the given zeros. degree \(4 ; 2,1,-3\) (multiplicity 2)

Find the vertical and slant asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph \(f\). $$ f(x)=\frac{x^{3}-8}{x^{2}-x} $$

Find all real zeros of the given polynomial function \(f\). Then factor \(f(x)\) using only real numbers. $$ f(x)=16 x^{5}-24 x^{4}+25 x^{3}+39 x^{2}-23 x+3 $$