91Ó°ÊÓ

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. \(f(x)=(x+3)^{2}-4\)

Determine whether the statement is true or false. Justify your answer. The graph of a quadratic model with a negative leading coefficient will have a maximum value at its vertex.

Find any asymptotes and holes in the graph of the rational function. Verify your answers by using a graphing utility. $$f(x)=\frac{x^{2}+2 x+1}{2 x^{2}-x-3}$$

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.) $$f(x)=x^{2}+36$$

Use long division to divide. $$\frac{x^{4}}{(x-1)^{3}}$$

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. $$g(x)=\frac{1}{x+2}+2$$

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) \(g(x)=(x+4)^{3}+1\)

Describe the graph of the function and identify the vertex. Use a graphing utility to verify your results. \(f(x)=(x-7)^{2}+2\)

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.) $$f(x)=16 x^{4}-81$$