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Home Question Bank Math Pre Calculus Archive 2024 November 11

Pre-calculus Questions from Nov 11,2024

Browse the Pre-calculus Q&A Archive for Nov 11,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Use the graph of \( y=f(x) \) shown below to graph the function \( g(x)=f\left(\frac{1}{2} x\right) \) Find all asymptotes and holes, for the given \( g(t)=\frac{3 x^{2}-21 x}{\left(x^{2}-25\right)\left(x^{2}+5 x-84\right)} \) 9. Construa o gráfico das funções exponenciais a seguir. \( \begin{array}{ll}\text { a) } f(x)=5^{x} & \text { c) } h(x)=\left(\frac{1}{4}\right)^{x} \\ \text { b) } g(x)=\left(\frac{1}{3}\right)^{x} & \text { d) } i(x)=4^{x}\end{array} \) 9. Construa o gráfico das funções exponenciais a seguir. \( \begin{array}{ll}\text { a) } f(x)=5^{x} & \text { c) } h(x)=\left(\frac{1}{4}\right)^{x} \\ \text { b) } g(x)=\left(\frac{1}{3}\right)^{x} & \text { d) } i(x)=4^{x}\end{array} \) 1. Interpolación de LaGrange Utiliza la interpolación de Lagrange para encontrar el polinomio que pasa por los siguientes conjuntos de puntos. Después, demuestre de forma gráfica con GeoGebra que cada punto pertenece al polinomio que construyo. a) \( (-2,4),(1,-3),(3,7) \) Realizamos la tabla para identificar el polinomio de LaGrange Puntos A jet is flying through a wind that is blowing at a speed of \( 88 \mathrm{~km} / \mathrm{h} \) in the direction N \( 60^{\circ} \mathrm{E} \). The jet has a speed of \( 1224 \mathrm{~km} / \mathrm{h} \) relative to the air, and the pilot heads the jet in the direction \( \mathrm{N} 60^{\circ} \mathrm{W} \). Find the speed and direction of the jet, correct to one decimal place. \( f^{-1}(x)=\frac{2}{x} \) The domain of \( f \) is \( (-\infty, 0) \cup(0, \infty) \) and the range of \( f \) is \( (-\infty, 0) \cup(0, \infty) \) (Type your answers in interval notation.) The domain of \( f^{-1} \) is \( \square \) and the range of \( f^{-1} \) is (Type your answers in interval notation.) \( f^{1}(x)=\frac{2}{x} \) The domain of \( f \) is \( \square \) and the range of \( f \) is (Type your answers in interval notation.) Find the inverse of the following one-to-one function. Give the domain and the range of \( f \) and of \( f^{-1} \), and then graph both \( f \) and \( f^{-1} \) on the same set of axes. \( f(x)=\frac{2}{x} \) \( f^{-1}(x)=\frac{2}{x} \) The domain of \( f \) is \( \square \) and the range of \( f \) is (Type your answers in interval notation.) The population of a country is modeled by the function \( P(t)=15.9 e^{0.01462 t} \) where \( P(t) \) is the population (in millions) \( t \) years after January 1,2000 . Use the model to predict the year during which year the population will reach 30 million if this trend continues.
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