91Ó°ÊÓ

Describe the graph of the function and identify the vertex. Use a graphing utility to verify your results. \(f(x)=-6-\frac{1}{4} x^{2}\)

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) \(g(x)=(x-2)^{3}-3\)

Use long division to divide. $$\left(x^{5}+7\right) \div\left(x^{3}-1\right)$$

Find any asymptotes of the graph of the rational function. Verify your answers by using a graphing utility to graph the function. $$f(x)=\frac{x^{2}-4 x}{x^{2}-4}$$

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. $$P(x)=\frac{1-3 x}{1-x}$$

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.) $$f(x)=x^{2}+6 x-2$$

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.) $$f(x)=x^{2}+25$$

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

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. $$f(t)=\frac{1-2 t}{t}$$

Describe the graph of the function and identify the vertex. Use a graphing utility to verify your results. \(f(x)=(x+3)^{2}-4\)