Pre-calculus Questions from Dec 23,2024

Browse the Pre-calculus Q&A Archive for Dec 23,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Graph the tunction. Give the equations of the vertical and horizontal asymptotes. \( y=\frac{2 x}{\mathrm{x}-4} \) Give the equations of any vertical asymptotes for the graph of the rational function. Select the correct choice and, if necessary, fil in the answer box(es) within your choice. A. The function has one vertical asymptote. The vertical asymptote is (Simplify your answer. Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymplote is (Simplify your answers. Type equations.) C. There is no vertical asymptote. What is the y-intercept of the exponential function \( f(x) = 2^x \)? The annual amount of energy produced in a country from dry natural gas (in trilion cubic feet) can be approximated by the function \( 9(t)=16.3(1.025)^{\mathrm{t}} \), where \( \mathrm{t}=10 \) corresponds to the year 2010 . (a) Find the amount of dry natural gas energy produced in 2018 . (b) If the model continues to be accurate, project the amount of dry natural gas energy produced in 2025 . (a) The amount of dry natural gas energy produced in 2018 was trilion cubic feet. (Round to two decimal places as needed.) (b) If the model continues to be accurate, the amount of dry natural gas energy that will be produced in 2025 is (Round to two decimal places as needed.) Consider the function \( f(x) = \sqrt{x} \). Describe how you would graph its inverse, and explain any transformations that occur. Determina si la gráfica de la función \( h(x) = -\sqrt{x} + 4 \) representa una función inversa válida para su correspondiente función cuadrática. Justifica tu respuesta. Exercice 4.3. Pour tout entier \( \mathrm{n} \geq 1 \), on définit : \( \mathrm{t}_{\mathrm{n}}=\sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{k}=\frac{\mathrm{n}(\mathrm{n}+1)}{2} \). Démontrer que, pour tol entier \( \mathrm{n} \geq 1 \), on \( \mathrm{a}: \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{t}_{\mathrm{k}}=\frac{1}{6} \mathrm{n}(\mathrm{n}+1)(\mathrm{n}+2) \). The range of the function \( f(x)=\sin 3 x-\frac{3}{4} \cos 3 x-1 \) is كيف يمكن تحديد إذا كانت دالتين هما دوال معكوسة لبعضهما باستخدام الفكر الإجرائي للرسوم البيانية؟ ¿Cuál es el punto medio de \( f(x)=x^{2}+1 \) en el intervalo \( \{1,3\rceil \) ? a. 9 b. 6,72 c. \( 16 / 3 \) d. 3,67 What is the amplitude of \( g(x)=-2 \sin \left(\frac{\pi}{2} x-3\right)+5 ? \)
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