91Ó°ÊÓ

Find all the zeros of the function and write the polynomial as a product of linear factors. Use a graphing utility to verify your results graphically. (If possible, use the graphing utility to verify the imaginary zeros.) $$g(x)=x^{2}+10 x+23$$

Describe the graph of the function and identify the vertex. Use a graphing utility to verify your results. \(f(x)=x^{2}+8\)

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) \(g(x)=x^{3}-3\)

Use long division to divide. $$\left(1+3 x^{2}+x^{4}\right) \div\left(3-2 x+x^{2}\right)$$

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) \(g(x)=-x^{3}+4\)

Sketch the graph of the rational function by hand. As sketching aids, check for intercepts, vertical asymptotes, horizontal asymptotes, and holes. Use a graphing utility to verify your graph. $$C(x)=\frac{5+2 x}{1+x}$$

Find any asymptotes of the graph of the rational function. Verify your answers by using a graphing utility to graph the function. $$f(x)=\frac{2 x^{2}}{x^{2}+x-6}$$

Describe the graph of the function and identify the vertex. Use a graphing utility to verify your results. \(f(x)=\frac{1}{2} x^{2}-5\)

Find all the zeros of the function and write the polynomial as a product of linear factors. Use a graphing utility to verify your results graphically. (If possible, use the graphing utility to verify the imaginary zeros.) $$f(x)=x^{2}-12 x+26$$

Use long division to divide. $$\left(x^{3}-9\right) \div\left(x^{2}+1\right)$$