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. $$r(x)=\frac{4 x^{2}}{x^{2}-2 x-3}$$

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

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

A polynomial \(P\) is given. (a) Find all the real zeros of \(P .\) (b) Sketch a graph of \(P\).0 x+9. $$P(x)=-x^{4}+10 x^{2}+8 x-8$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. State the domain and range. $$y=x^{4}-18 x^{2}+32, \quad[-5,5] \text { by }[-100,100]$$

Show that the given value(s) of \(c\) are zeros of \(P(x),\) and find all other zeros of \(P(x)\). $$P(x)=3 x^{4}-8 x^{3}-14 x^{2}+31 x+6, \quad c=-2,3$$

Find all zeros of the polynomial. $$P(x)=4 x^{4}+4 x^{3}+5 x^{2}+4 x+1$$

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. $$r(x)=\frac{5 x^{2}+5}{x^{2}+4 x+4}$$

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

A polynomial \(P\) is given. (a) Find all the real zeros of \(P .\) (b) Sketch a graph of \(P\).0 x+9. $$P(x)=x^{5}-x^{4}-5 x^{3}+x^{2}+8 x+4$$