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Home Question Bank Math Pre Calculus Archive 2024 November 30

Pre-calculus Questions from Nov 30,2024

Browse the Pre-calculus Q&A Archive for Nov 30,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find the domain and range of the inverse of the given function. \( f(x)=-\frac{9}{x} \) A. Domain: \( (-\infty, 0) \cup(0, \infty) \); range: \( (-\infty, 0) \) B. Domain and range: \( (-\infty, 0) \cup(0, \infty) \) C. Domain: all real numbers; range: \( (-\infty, 0) \cup(0, \infty) \) D. Domain and range: all real numbers The population of a particular city is increasing at a rate proportional to its size. It follows the function \( \mathrm{P}(\mathrm{t})=1+\mathrm{k} e^{0.08 \mathrm{t}} \) where k is a constant and \( t \) is the time in years. If the current population is 11,000 , in how many years is the population expected to be 27,500 ? (Round to the nearest year.) A. 68 yr B. 11 yr C. 6 yr D. 5 yr Determine whether the function is one-to-one by graphing and using the horizontal line test. \( f(x)=\frac{x-10}{x-8} \) The population of a particular city is increasing at a rate proportional to its size. It follows the function \( \mathrm{P}(\mathrm{t})=1+\mathrm{ke} \mathrm{e}^{0.12 \mathrm{t}} \) where k is a constant and \( t \) is the time in years. If the current population is 30,000 , in how many years is the population expected to be 75,000 ? (Round to the nearest year.) A. 8 yr B. 3 yr D. 5 yr Graph the function. Describe its position relative to the graph of the indicated basic function. \( f(x)=e^{-x+6} ; \) relative to \( f(x)=e^{x} \) Aiminate the parameter. Write the resulting equation in s A hyperbola: \( x=h+a \sec t, y=k+b \tan t \) The equation in standard form is Eliminate the parameter, then write the resulting equ A circle \( x=h+r \cos t, y=k+r \sin t \) Determine whether the function is one-to-one by graphing and using the horizontal line test. \( f(x)=\frac{x-10}{x-6} \) Find the domain and range of the inverse of the given function. \( f(x)=-\frac{3}{x} \) A. Domain: all real numbers; range: \( (-\infty, 0) \cup(0, \infty) \) B. Domain: \( (-\infty, 0) \cup(0, \infty) ; \) range: \( (-\infty, 0) \) C. Domain and range: \( (-\infty, 0) \cup(0, \infty) \) D. Domain and range: all real numbers Graph all vertical and horizontal asymptotes of the rational function. \[ f(x)=\frac{-10}{-x-5} \]
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