91Ó°ÊÓ

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $$8 i$$

Write the function in the form \(f(x)=(x-k) q(x)+r(x)\) for the given value of \(k\). Use a graphing utility to demonstrate that \(f(k)=r\). Value of \(k\) \(k=4\) \(k=-\frac{2}{3}\) \(k=\sqrt{2}\) \(k=-\sqrt{5}\) \(k=1-\sqrt{3}\) \(k=2+\sqrt{2}\) Function $$f(x)=15 x^{4}+10 x^{3}-6 x^{2}+14$$

Use a graphing utility to graph the function. Determine its domain and identify any vertical or horizontal asymptotes. $$g(x)=-\frac{x}{(x-2)^{2}}$$

(a) find all zeros of the function, (b) write the polynomial as a product of linear factors, and (c) use your factorization to determine the \(x\) -intercepts of the graph of the function. Use a graphing utility to verify that the real zeros are the only \(x\) -intercepts. $$f(x)=2 x^{3}-3 x^{2}+8 x-12$$

(a) find the zeros algebraically, (b) use a graphing utility to graph the function, and (c) use the graph to approximate any zeros and compare them with those from part (a). \(g(t)=\frac{1}{2} t^{4}-\frac{1}{2}\)

Write the function in the form \(f(x)=(x-k) q(x)+r(x)\) for the given value of \(k\). Use a graphing utility to demonstrate that \(f(k)=r\). Value of \(k\) \(k=4\) \(k=-\frac{2}{3}\) \(k=\sqrt{2}\) \(k=-\sqrt{5}\) \(k=1-\sqrt{3}\) \(k=2+\sqrt{2}\) Function $$f(x)=x^{3}+3 x^{2}-2 x-14$$

Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result. Vertex: (-2,5) Point: (0,9)

Find the zeros (if any) of the rational function. Use a graphing utility to verify your answer. $$g(x)=1+\frac{6}{x-3}$$

Use a graphing utility to graph the function. Determine its domain and identify any vertical or horizontal asymptotes. $$f(x)=\frac{x+1}{x^{2}-x-6}$$

(a) find all zeros of the function, (b) write the polynomial as a product of linear factors, and (c) use your factorization to determine the \(x\) -intercepts of the graph of the function. Use a graphing utility to verify that the real zeros are the only \(x\) -intercepts. $$f(x)=2 x^{3}-5 x^{2}+18 x-45$$