Choose the end behavior of the graph of each polynomial function. \begin{tabular}{ll}\hline (a) \( f(x)=4 x^{3}-3 x^{2}+5 x+3 \) & Falls to the left and rises to the right \\ Rises to the left and falls to the right \\ Rises to the left and rises to the right \\ Falls to the left and falls to the right \end{tabular}

\( s \) denotes the length of the arc of a circle of radius \( r \) subtended by the central angle \( \theta \). Find the missing quantity. \( r=40 \) inches, \( \theta=51^{\circ}, \mathrm{s}= \) ? \( \mathrm{s}=\square \) (Type an integer or decimal rounded to three decimal places as needed.)

The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and t is the time in years, express N as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using t as the variable and in terms of \( e \).) (b) If the population doubled in size over 19 months and the current population is 50,000 , what will the population be 3 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

How many turning points can a polynomial of degree 5 have at most?

Clarence is working in a lab testing bacteria populations. After starting out with a population of 259 bacteria, he observes the change in population and notices that the population triples every 14 minutes. Step 1 of 2 : Find the equation for the population \( P \) in terms of time \( t \) in minutes. Round values to three decimal places. Answer

Suppose that the function \( h \) is defined on the interval \( (-2,2] \) as follows. \[ h(x)=\left\{\begin{array}{ll}-1 & \text { if }-2<x \leq-1 \\ 0 & \text { if }-1<x \leq 0 \\ 1 & \text { if } 0<x \leq 1 \\ 2 & \text { if } 1<x \leq 2\end{array}\right. \] Find \( h(-1), h(-0.5) \), and \( h(1) \). \( h(-1)=\square \) \( h(-0.5)=\square \)