91Ó°ÊÓ

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a polynomial inequality that has a value for which the polynomial function is undefined.

To write an equation of a polynomial function with the given characteristics Use a graphing utility to graph your function to see if you are correct. If not, modify the function's equation and repeat this process. Touches the \(x\) -axis at 0 and crosses the \(x\) -axis at \(2 ;\) lies below the \(x\) -axis between 0 and 2.

A tourist drives 90 miles along a scenic highway and then takes a 5-mile walk along a hiking trail. The average velocity driving is nine times that while hiking. Express the total time for driving and hiking, \(T,\) as a function of the average velocity on the hike, \(x\).

Divide 737 by 21 without using a calculator. Write the answer as quotient \(+\frac{\text { remainder }}{\text { divisor }}\)

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 \(x \rightarrow-2^{+}\).

Describe how to graph a rational function.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of a rational function can never cross a vertical asymptote.

Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=3,\) a horizontal asymptote \(y=0, y\) -intercept at \(-1,\) and no \(x\) -intercept.