The polynomial function \( f(x)=x^{3}-9 x \) is multiplied by \( \frac{-1}{3} \) to produce the function \( g(x)=-\frac{1}{3} x^{3}+3 x \). Which of the following is true about the \( [ \) Window] settings for the graph of \( g(x) \) ? A Multiply the \( X_{\min \text { and }} X_{\max } \) from \( f(x) \) by \( -\frac{1}{3} \). B Multiply the \( Y_{\min \text { and }} Y_{\max } \) from \( f(x) \) by \( -\frac{1}{3} \). C Multiply the \( X_{\min ,} X_{\max }, Y_{\min } \), and \( Y_{\max } \) from \( f(x) \) by \( -\frac{1}{3} \). D Keep the settings from \( f(x) \).

Which function transforms the translating it up 5 units? (1 point) \( g(x)=-2^{x+5} \) \( g(x)=2^{-x+5} \) \( g(x)=-2^{x}+5 \) \( g(x)=2^{-x}+5 \)

A population of bacteria is growing according to the equation \( P(t)=850 e^{0.03 t} \). Use a graphing calculator to estimate when the population will exceed 924. \( t=\square \) Give your answer accurate to one decimal place.

A wooden artifact from an ancient tomb contains 30 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years

\( f(x)=3 e^{x+1} \), for \( x=-4 \) Your answer is \( f(-4)=\square \)

Sketch the graph of a polynomial function with roots at \( 2 \) (multiplicity 1), \( -3 \) (multiplicity 2), and \( 4 \) (multiplicity 3). Describe how each root affects the shape of the graph.