91Ó°ÊÓ

Will help you prepare for the material covered in the next section. Divide 737 by 21 without using a calculator. Write the answer as quotient \(+\frac{\text { remainder }}{\text { divisor }}\)

a. If \(y=k x^{2},\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x^{2}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)

a. If \(y=\frac{k}{x},\) find the value of \(k\) using \(x=8\) and \(y=12\) b. Substitute the value for \(k\) into \(y=\frac{k}{x}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=3\)

Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2^{-}\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\)

Will help you prepare for the material covered in the next section. Rewrite \(4-5 x-x^{2}+6 x^{3}\) in descending powers of \(x\)

Will help you prepare for the material covered in the next section. Use $$\frac{2 x^{3}-3 x^{2}-11 x+6}{x-3}=2 x^{2}+3 x-2$$ to factor \(2 x^{3}-3 x^{2}-11 x+6\) completely.

If you are given the equation of a rational function, explain how to find the vertical asymptotes, if any, of the function's graph.

If you are given the equation of a rational function, explain how to find the horizontal asymptote, if there is one, of the function's graph.

Describe how to graph a rational function.

If you are given the equation of a rational function, how can you tell if the graph has a slant asymptote? If it does, how do you find its equation?