Pre Calculus Questions & Answers

5. Dada la función exponencial \( h(x)=e^{\wedge}(2 x) \), ¿cuál es el valor de \( h(1) \) ? \( h(1)=e / 2 \) \( h(1)=e \) \( h(1)=2 e \)

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. \( g(x)=3^{x}-1 \) B. The graph of \( f(x)=3^{x} \) should be shifted 1 unit upward. C. The graph of \( f(x)=3^{x} \) should be shifted 1 unit to the right. Graph \( g(x)=3^{x}-1 \) and its asymptote. Use the graphing tool to graph the function as a \( f(x)=3^{x} \) should be shifted 1 unit downward. solid curve and the asymptote as a dashed line. The equation of the asymptote for \( g(x)=3^{x}-1 \) is The . (Type an equation.)

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. \( g(x)=3^{x}-1 \) Which transformation is needed to graph the function \( g(x)=3^{x}-1 \) ? Choose the correct answer below. B. The graph of \( f(x)=3^{x} \) should be shifted 1 unit to the left. C. The graph of \( f(x)=3^{x} \) should be shifted 1 unit upward. D. The graph of \( f(x)=3^{x} \) should be shifted 1 unit downward.

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 ( \( \left.-\infty, \infty\right) \). (Type your answer in interval notation.) The range of \( g(x)=3^{x-6} \) is \( \square \). (Type your answer in interval notation.)

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 \( \begin{array}{c}\square=2\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right) \\ z=2\left(\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}\right) \\ z=2\left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right) \\ \square=2\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)\end{array} \) \( \begin{array}{l}\square \quad\end{array} \)