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Home Question Bank Math Pre Calculus Archive 2024 November 13

Pre-calculus Questions from Nov 13,2024

Browse the Pre-calculus Q&A Archive for Nov 13,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( g(x)=\left(\frac{4}{5}\right)^{x-2}+9 \) a) Choose the correct parent function. O \( y=\left(\frac{5}{4}\right)^{x} \) \( y=\left(\frac{4}{5}\right)^{x} \) \( y=\log _{\frac{5}{4}}(x) \) \( y=\log _{\frac{4}{5}}(x) \) b) Choose the correct transformation (Reflections). Select an answer c) Choose the correct transformation (Stretches/Compressions). Select an answer d) Choose the correct transformation (Vertical Shifts). Select an answer e) Choose the correct transformation (Horizontal Shifts). Select an answer a) Choose the correct parent function. \( y=2^{x} \) \( y=\left(\frac{1}{2}\right)^{x} \) \( y=\log _{2}(x) \) \( y=\log _{\frac{1}{2}}(x) \) b) Choose the correct transformation (Reflections). Select an answer c) Choose the correct transformation (Stretches/Compressions). Select an answer d) Choose the correct transformation (Vertical Shifts). Select an answer e) Choose the correct transformation (Horizontal Shifts). Select an answer A wooden artifact from an ancient tomb contains 40 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years For the graph of \( y=f(x) \), where \[ f(x)=\frac{2 x-7}{x^{2}-25} \] (a) Identify the \( x \)-intercepts. (b) Identify the vertical asymptotes. (c) Identify the horizontal asymptotes or slant asymptote if applicable. (d) Identify the \( y \)-intercept. La parametrización \( (1+3 \operatorname{Cos}(2 \mathrm{t}), 2+3 \operatorname{Sen}(2 \mathrm{t})) \) satisface el enunciado siguiente: Parametriza la trayectoria de un punto que gira en un círculo de radio 3 y centro en \( (1,2) \), partiendo del punto mas bajo y moviéndose en la dirección contraria a las manecillas del reloj con |rapidez constante 2. For the graph of \( y=f(x) \), where \[ f(x)=\frac{(3 x+5)(x+7)}{(x-1)(2 x-3)} \] (a) Identify the \( x \)-intercepts. (b) Identify any vertical asymptotes. (c) Identify the horizontal asymptote or slant asymptote if applicable. (d) Identify the \( y \)-intercept. Find an equation of a function that meets the given conditions. \[ \begin{array}{l}x \text {-intercepts: }(-5,0) \text { and }(-2,0) \\ \text { vertical asymptote: } x=2 \\ \text { horizontal asymptote: } y=1 \\ y \text {-intercept: }\left(0, \frac{5}{2}\right)\end{array} \] Draw the graph of \( f(x)=\left(\frac{1}{4}\right)^{x+5} \) Determine the vertical asymptotes of the graph of the function. \[ f(x)=\frac{x+4}{2 x^{2}-11 x+5} \] Separate multiple equations with commas as necessary. Select " Equation(s) of the vertical asymptote(s):
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