\begin{tabular}{l} Graph the following function and its inverse on the same \\ Cartesian plane. \\ \( f(x)=9^{\mathrm{x}} ; \mathrm{f}^{-1}(\mathrm{x})=\log _{9} \mathrm{x} \) \\ Use the graphing tool to graph the function. \\ \hline Click to \end{tabular}

What is the end behavior of the graph of the exponential function \( f(x)=b^{x} \) when \( 0<b<1 ? \) (1 point) \( f(x) \rightarrow \infty \) as \( x \rightarrow \infty, f(x) \rightarrow 0 \) as \( x \rightarrow-\infty \) \( f(x) \rightarrow 0 \) as \( x \rightarrow \infty, f(x) \rightarrow \infty \) as \( x \rightarrow-\infty \) \( f(x) \rightarrow \infty \) as \( x \rightarrow \infty ; f(x) \rightarrow-\infty \) as \( x \rightarrow 0 \) \( f(x) \rightarrow \infty \) as \( x \rightarrow 0 ; f(x) \rightarrow-\infty \) as \( x \rightarrow-\infty \)

The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 24200 . (a) Find a function that models the population \( t \) years after \( 2000(t=0 \) for 2000). Hint: Use an exponential function with base \( e \). Your answer is \( P(t)= \) (b) Use the function from part (a) to estimate the fox population in the year 2008 . Your answer is (the answer must be an integer)

What is a turning point in the context of polynomial graphs?

Draw the graph of \( f(x)=\log _{3}(x-3)+4 \)

Sketch a graph of the function \( f(x)=-3 \sin (3 x) \)