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Home Question Bank Math Pre Calculus Archive 2024 November 02

Pre-calculus Questions from Nov 02,2024

Browse the Pre-calculus Q&A Archive for Nov 02,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Graph the logarithmic function \( g(x)=-\log _{2} x+1 \). To do this, plot two points on the graph of the function, and also draw the asymptote. Then, click on the graph-a-function button. Additionally, give the domain and range of the function using interval notation. The decay constant for americium 241 is \( \mathrm{k}=-0.002108 \). If 5 milligrams ( mg ) of americium 241 is sealed in a laboratory container today, how much will be present in 500 years? The amount of americium 241 present in 500 years will be approximately (Round to the nearest whole number.) Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function. \( f(x)=7 x^{7}+4 x^{6}+7 x^{5}+7 \) A. Falls left \( \& \) rises right. B. Falls left \( \& \) falls right. C. Rises left \( \& \) rises right. D. Rises left \( \& \) falls right. E. None of the above. Consider the function \( f(x)=-2 x^{2}+20 x-5 \). a. Determine, without graphing. whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. a. The function has a Abusiness estimates that the value \( V(t) \) of a certain piece of office equipment is decreasing according to the function \( V(t)=50.2(0.9)^{\prime} \), where \( t \) represents the number of years that have elapsed sincel it was purchased, and \( \mathrm{V}(\mathrm{t}) \) is in dollars. Find this plece of equipment's value after 5 years. What is the value of the piece of equipment after 5 years? \( \$ \square \) (Round to the nearest cent as needed.) Given the function \( f(x)=x^{2}-14, x \geq 0 \), complete parts a through \( c \). (a) Find an equation for \( f^{-1}(x) \). (b) Graph \( f \) and \( f^{-1} \) in the same rectangular coordinate system. (c) Use interval notation to give the domain and the range of \( f \) and \( f^{-1} \). (a) Find \( f^{-1}(x) \). \( f^{-1}(x)= \) (Type an exact answer, using radicals as needed.) Describe the end behavior of the polynomial function \( g(x) = -2x^{5} + 6x^{2} - 3 \). For the polynomial function \( h(x) = 5x^4 - x^2 + 7 \), what is the end behavior as \( x \) approaches positive and negative infinity? \( f(x)=\sqrt{\frac{x^{3}}{x+2}} \) a) Tracer le tableau de raviatorns de \( f \). \( z = ( \frac { 1 + i \sqrt { 3 } } { \sqrt { 2 } - i \sqrt { 2 } } ) ^ { 15 } \)
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