91Ó°ÊÓ

Evaluate the expression and write the result in the form \(a+b i.\) $$i^{100}$$

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. $$r(x)=\frac{(x-1)(x+2)}{(x+1)(x-3)}$$

Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example \(3(a)\) $$P(x)=x^{4}-7 x^{3}+14 x^{2}-3 x-9$$

\(43-46=\) The graph of a polynomial function is given. From the graph, find (a) the \(x\) - and \(y\) -intercepts (b) the coordinates of all local extrema (GRAPH CAN'T COPY) $$P(x)=-\frac{1}{2} x^{3}+\frac{3}{2} x-1$$

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. $$r(x)=\frac{2 x(x+2)}{(x-1)(x-4)}$$

Use synthetic division and the Remainder Theorem to evaluate \(P(c)\). $$P(x)=-2 x^{6}+7 x^{5}+40 x^{4}-7 x^{2}+10 x+112, \quad c=-3$$

Find all zeros of the polynomial. $$P(x)=x^{3}-x-6$$

Evaluate the expression and write the result in the form \(a+b i.\) $$i^{1002}$$

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. $$r(x)=\frac{x^{2}-2 x+1}{x^{2}+2 x+1}$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer correct to two decimal places. $$y=-x^{2}+8 x, \quad[-4,12] \text { by }[-50,30]$$