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Home Question Bank Math Pre Calculus Archive 2024 December 03

Pre-calculus Questions from Dec 03,2024

Browse the Pre-calculus Q&A Archive for Dec 03,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Analyze the graph of the function. \( \mathrm{R}(\mathrm{x})=\frac{8 \mathrm{x}+8}{9 \mathrm{x}+27} \) A. \( \mathrm{x}=-3 \) (Use a comma to separate answers as needed. Type an integer or a fraction.) B. There is no vertical asymptote. (c) What is the equation of the horizontal or oblique asymptote of \( \mathrm{R}(\mathrm{x}) \) ? Select the correct choice below and fill in any answer boxes within your choice. A. \( \mathrm{y}=\square \) (Simplify your answer.) B. There is no horizontal or oblique asymptote. Analyze the graph of the function. \( R(x)=\frac{x+5}{x(x+14)} \) (a) What is the domain of \( R(x) \) ? A. \( \{x \mid x \neq 0 \) and \( x \neq-14 \) and \( x \neq-5\} \) B. \( \{x \mid x \neq 0 \) and \( x \neq-14\} \) C. \( \{x \mid x \neq 0 \) and \( x \neq-5\} \) D. All real numbers Sketch the graph of \( y = \log_{10}(x) \) and identify its intercepts. Construa o gráfico de \( f(x)=\left\{\begin{array}{l}x-1 \text {, se } x>2 \\ 2-x, \text { se } x<2\end{array}\right. \) 8. Consider the polar curve given by the equation \( r=2 \sin (\theta) \) a) (7pts) The point \( \left(\sqrt{2}, \frac{\pi}{4}\right) \) is a point on this polar curve. Determine the \( x \) )-coordinates of this point. b) (8pts) Represent this curve as a parametric curve (with parameter \( \theta \) ). c) (8pts) Set up, but do not evaluate, an integral which represents the area enclosed by this curve. 8. Consider the polar curve given by the equation \( r=2 \sin (\theta) \) a) \( (7 \mathrm{pts}) \) The point \( \left(\sqrt{2}, \frac{\pi}{4}\right) \) is a point on this polar curve. Determine the \( x y \)-coordinates of this point. b) (8pts) Represent this curve as a parametric curve (with parameter \( \theta \) ). Determine the vertical asymptotes of the graph of the fun \[ h(a)=\frac{a-3}{4 a^{2}-9 a+2} \] Separate multiple equations with commas as necessary. 3. Un granjero tiene 200 metros de cerca con la cual puede delimitar un terreno rectangular. Un lado del terreno puede aprovechar una cerca ya existente. ¿Cuál es el área máxima que puede cercarse? 0. A funçấo \( f: I R \rightarrow I R \), de lei \[ f(x)=2+3 \cdot \cos x \] tem seu conjunto imagem dado por A) \( \varnothing \) B) \( I R \) C) \( [-1,5] \) D) \( [-5,1] \) E) \( [-1,1] \) Find the foci of the hyperbola. \[ -9 x^{2}+y^{2}+54 x-90=0 \]
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