The function \( f(x)=x^{3}-5 \) is one-to-one. (a) Find the inverse of \( f \) and check the answer. (b) Find the domain and the range of \( f \) and \( f^{-1} \). (c) Graph \( f, f^{-1} \), and \( y=x \) on the same coordinate axes. (a) \( f^{-1}(x)=\square \) (Simplify your answer. Use integers or fractions for any numbers in the expression.)

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)

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.

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

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.

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