91Ó°ÊÓ

Find the intercepts and asymptotes, and then sketch a graph of the rational function and state the domain and range. Use a graphing device to confirm your answer. $$r(x)=\frac{2 x^{2}+10 x-12}{x^{2}+x-6}$$

Find the local maximum and minimum values of the function and the value of \(x\) at which each occurs. State each answer correct to two decimal places. $$g(x)=x^{4}-2 x^{3}-11 x^{2}$$

Show that the given value(s) of \(c\) are zeros of \(P(x)\), and find all other zeros of \(P(x)\). $$P(x)=x^{3}-x^{2}-11 x+15, \quad c=3$$

Find all zeros of the polynomial. $$P(x)=x^{4}-6 x^{3}+13 x^{2}-24 x+36$$

Find all solutions of the equation and express them in the form \(a+b i\) $$x^{2}+49=0$$

Find all solutions of the equation and express them in the form \(a+b i\) $$9 x^{2}+4=0$$

Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example \(3(a)\) $$P(x)=-x^{3}-2 x^{2}+5 x+6$$

Show that the given value(s) of \(c\) are zeros of \(P(x)\), and find all other zeros of \(P(x)\). $$P(x)=3 x^{4}-x^{3}-21 x^{2}-11 x+6, \quad c=\frac{1}{3},-2$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. $$y=x^{5}-5 x^{2}+6, \quad[-3,3] \text { by }[-5,10]$$

Find the intercepts and asymptotes, and then sketch a graph of the rational function and state the domain and range. Use a graphing device to confirm your answer. $$r(x)=\frac{2 x^{2}+2 x-4}{x^{2}+x}$$