91Ó°ÊÓ

Find the long run behavior of each function as \(x \rightarrow \infty\) and \(x \rightarrow-\infty\) \(f(x)=x^{4}\)

Find the \(C\) and \(t\) intercepts of each function \(C(t)=2 t(t-3)(t+1)^{2}\)

For each function, find the \(x\) intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptote. Use that information to sketch a graph. $$ p(x)=\frac{2 x-3}{x+4} $$

For each of the follow quadratics, find a) the vertex, b) the vertical intercept, and \(c\) ) the horizontal intercepts. $$ y(x)=2 x^{2}+10 x+12 $$

Find the degree and leading coefficient of each polynomial \(4 x^{7}\)

Write an equation for a rational function with the given characteristics Vertical asymptote at \(x=3\) Double zero at \(x=1 \quad y\) intercept at (0,4)

A scientist has a beaker containing \(20 \mathrm{~mL}\) of a solution containing \(20 \%\) acid. To dilute this, she adds pure water. a. Write an equation for the concentration in the beaker after adding \(n\) mL of water b. Find the concentration if \(10 \mathrm{~mL}\) of water is added c. How many \(\mathrm{mL}\) of water must be added to obtain a \(4 \%\) solution? d. What is the behavior as \(n \rightarrow \infty,\) and what is the physical significance of this?

A rectangle is inscribed with its base on the \(x\) axis and its upper corners on the curve \(y=16-x^{4}\). What are the dimensions of such a rectangle with the greatest possible area?