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Home Question Bank Math Pre Calculus Archive 2024 November 22

Pre-calculus Questions from Nov 22,2024

Browse the Pre-calculus Q&A Archive for Nov 22,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find all vertical asymptotes of the following function. \[ f(x)=\frac{5 x^{2}-12 x-9}{2 x^{2}-16 x+30} \] Find all vertical asymptotes of the following function. \[ f(x)=\frac{2 x^{2}-17 x+8}{2 x^{2}-18 x} \] Determine si las siguientes sucesiones son monótonas. Explique el procedimiento \( \{\cos n \pi\} \) Obtenga el dominio de cada función. Justificar, no solo escribir la respuesta. 1. \( \mathbf{g}(\mathrm{X})=\sqrt{4-X} \) Determine si las siguientes sucesiones son monótonas. Explique el procedimiento a) \( \left\{\frac{1-2 n}{n^{2}}\right\} \) Oada la función \( f(x)=\frac{x^{2}}{x+1} \quad \) para un dominio de \( \{0,1,3 \) y 5\( \} \) el rango esperado es: a. \( \{0,1.5,3.2, y \) 7.1\}. b. \{indeterminada, \( 0,-4, y-5.3\} \) c. \{indeterminada, \( 0,2.2 \) y 7.1\( \} \) d. \( \{0,0.5,2.2 \) y 4.1\( \} \) Question Find the domain of the function \( g(z)=\sqrt{\frac{3}{z+4}} \). (Write the domain in interval notation.) a) Defina función. Si la función \( f \) esta dada por la expresión \( y=f(x) \), explique quien sería el dominio y rango de \( f \). Escribe el dominio de la función \( f(x)=\frac{\sqrt{x^{2}-16}}{x+3} \). b) Enuncie dos tipos de transformaciones en la gráfica de una función. Ejemplifique. c) Defina función logaritmica. Determine su dominio y su imagen. Grafique un ejemplo. How does the graph of \( g(x)=3^{x}-2 \) compare to the graph of \( f(x)=3^{x} \) ? The graph of \( g(x) \) is a translation of \( f(x) 2 \) units left. The graph of \( g(x) \) is a translation of \( f(x) 2 \) units right. The graph of \( g(x) \) is a translation of \( f(x) 2 \) units up. The graph of \( g(x) \) is a translation of \( f(x) 2 \) units down. The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures? \( \sum_{n=1}^{15} 1(3)^{n-1} \) \( \sum_{n=1}^{15} 3(1)^{n-1} \) \( \sum_{n=1}^{15} 1\left(\frac{1}{3}\right)^{n-1} \) \( \sum_{n=1}^{15} \frac{1}{3}(1)^{n-1} \)
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