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. $$r(x)=\frac{-x^{2}+8 x-18}{x^{2}-8 x+16}$$

Use synthetic division and the Remainder Theorem to evaluate \(P(c)\). $$P(x)=x^{7}-3 x^{2}-1, \quad c=3$$

Finding Quadratic Functions Find a function \(f\) whose graph is a parabola with the given vertex and that passes through the given point. $$\text { Vertex }(2,-3) ; \quad \text { point }(3,1)$$

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. $$P(x)=x^{3}-7 x^{2}+17 x-15$$

Finding Quadratic Functions Find a function \(f\) whose graph is a parabola with the given vertex and that passes through the given point. $$\text { Vertex }(-1,5) ; \quad \text { point }(-3,-7)$$

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

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

Use a graphing device to solve the inequality, as in Example 5. Express your answer using interval notation, with the endpoints of the intervals rounded to two decimals. $$5 x^{4}<8 x^{3}$$

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. $$s(x)=\frac{4 x-8}{(x-4)(x+1)}$$