Pre Calculus Questions & Answers

Use transformations of the graph of \( f(x)=3^{x} \) to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x-6} \) Graph \( g(x)=3^{x-6} \) and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line. The equation of the asymptote for \( g(x)=3^{x-6} \) is \( y=0 \). (Type an equation.) The domain of \( g(x)=3^{x-6} \) is (Type your answer in interval notation.)

Begin by graphing \( f(x)=3^{x} \). Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x+6} \) C. The graph of \( f(x)=3^{x} \) should be shifted 6 units upward. D. The graph of \( f(x)=3^{x} \) should be shifted 6 units to the right. solid curve and the asymptote as a dashed line. The equation of the asymptote for \( g(x)=3^{x+6} \) is \( y=0 \). (Type an equation.) The domain of \( g(x)=3^{x+6} \) is (Type your answer in interval notation.)

If the population of squirrels on campus \( t \) years after the beginning of 1855 is given by the logistic growth fun \[ s(t)=\frac{3000}{1+12 e^{-1.08 t}} \] find the time \( t \) such that \( s(t)=2400 \). Time, \( t=3.58 \) which when rounded to two decimal places, corresponds to the year 1859

Begin by graphing \( f(x)=3^{x} \). Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x+6} \) C. The graph of \( f(x)=3^{x} \) should be shifted 6 units to the left. D. The graph of \( f(x)=3^{x} \) should be shifted 6 units upward. Graph \( g(x)=3^{x+6} \) and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line. The should be shifted 6 units to the right. The equation of the asymptote for \( g(x)=3^{x+6} \) is \( \square \). (Type an equation.)

Convert \( z=-1-i \sqrt{3} \) to polar form \( z=2\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right) \) \( z=2\left(\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}\right) \) \( \square=2\left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right) \) \( \square=2\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right) \)

Convert \( z=-1-i \sqrt{3} \) to polar form \( \begin{array}{c}\square=2\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right) \\ z=2\left(\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}\right) \\ z=2\left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right) \\ \square=2\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)\end{array} \) \( \begin{array}{l}\square \quad\end{array} \)

Math 110 Course Resources - Exponential \& Logarithmic Functions Course Packet on logistic growth If the population of squirrels on campus \( t \) years after the beginning of 1855 is given by the logistic growth function \( s(t)=\frac{3000}{1+12 e^{-1.08 t}} \) find the time \( t \) such that \( s(t)=2400 \). Time, \( t=\square \)

Match the function with its graph \[ f(x)=\sqrt{2 x} \] The correct graph is

Match the sequence or function with its graph. \[ a_{n}=\sqrt{2 n} \] The correct graph is

Match the sequence or function with its graph. \[ a_{n}=\sqrt{2 n} \]