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Home Question Bank Math Pre Calculus Archive 2025 January 17

Pre-calculus Questions from Jan 17,2025

Browse the Pre-calculus Q&A Archive for Jan 17,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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10. The atmospheric pressure in millibars at altitude \( x \) meters can be approximated by the following function. The function is valid for values of \( x \) between 0 and 10,000 . \[ f(x)=1038(1.000134)^{-x} \] 27. \( \left(3 \operatorname{cis} 15^{\circ}\right)\left(2 \operatorname{cis} 75^{\circ}\right) \) มีค่าตรงกับข้อใด ก. 6 ข. -6 ค. -6 i Follow the steps for graphing a rational function to graph the function \( R(x)=\frac{x^{2}}{x^{2}-x-20} \). I he runction nas inree venical asympiotes. I ne iermosi asympiote is \( \qquad \) , the miage as and the rightmost asymptote is \( \square \) (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote. Determine the behavior of the graph on either side of any vertical asymptotes, if one exists. Sele choice below and, if necessary, fill in the answer box(es) within your choice. A. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and \( -\infty \) on the other. It appro or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) . (Type integers or simplified fractions. Use a comma to separate answers as needed. Type only once.) B. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Tyf only once.) C. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and \( -\infty \) on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type only once.) D. There is no vertical asymptote. Follow the steps for graphing a rational function to graph the function \( R(x)=\frac{x^{2}}{x^{2}-x-20} \). ine runcuon nas uree verucar asympiotes. I ne ientmost asympiote is \( \qquad \) , ine miagie asympiote is and the rightmost asymptote is \( \square \) . (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote. Determine the behavior of the graph on either side of any vertical asymptotes, if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and \( -\infty \) on the other. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) ]. (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) . (Type an integer or a simplified fraction. Use a comma to only once.) It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) (Type an integer or a simplified fraction , (Type an int only once.) \( \square \) and - \( \infty \) on the other. D. There is no vertical asymptote. Question 1 How can you tell whether multiplying a constant by the parent function will result in a horizontal dilation? \( \begin{array}{ll}\text { O) If the constant is grouped with } x \text {, the result will be a horizontal dilation. } \\ \text { B) If the constant is greater than } 1 \text {, the result will be a horizontal dilation. } \\ \text { C) if the constant is between } 0 \text { and } 1 \text {, the result will be a horizontal dilation. }\end{array} \) 23.กำหนด \( f(x)=3^{-x} \) และ \( g(x)=2^{x} \) จงหาค่าของ \( \operatorname{fog}(1) \) ก. \( 3^{-2} \) ข. \( 2^{-3} \) ค. \( 3^{2} \) ง. \( 2^{3} \) 22.กำหนด \( f(x)=3^{-x} \) และ \( g(x)=2^{x} \) จงหาค่าของ \( \operatorname{gof}(-1) \) ก. \( 3^{-2} \) ข. \( 2^{-3} \) ค. \( 3^{2} \) ง. \( 2^{3} \) 17.ข้อใดต่อไปนี้เป็นฟังก์ชันเพิ่ม ก. \( y=\left(\frac{1}{2}\right)^{-x} \) ข. \( y=2^{-x} \) ค. \( y=\left(\frac{3}{4}\right)^{x} \) ง. \( y=\left(\sin 2^{o}\right)^{x} \) Analyze the polynomial function \( f(x)=(x+4)^{2}(1-x) \) using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function. The graph of \( f \) behaves like \( y=\square \) for large values of \( |x| \).
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