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Home Question Bank Math Pre Calculus Archive 2024 December 10

Pre-calculus Questions from Dec 10,2024

Browse the Pre-calculus Q&A Archive for Dec 10,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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3) Disegnare il grafico di una funzione \( f(x) \) che soddisfi le seguenti cundizionit - Dominio R - \( \lim _{x \rightarrow-\infty} f(x)=-2 \) - \( f(0)=5 \) - \( \lim _{x \rightarrow+\infty} f(x)=0 \) 1) Realicen el gráfico aproximado de las siguientes funciones: a) \( f(x)=x^{3}+x^{2}-x-2 \) What is the domain and range of the logarithmic function \( y = \log(x) \)? Domain of the function \( R(x)=\log x \) \( x \) 1. The graph of \( y=-3 x^{2} \) shifted 2 units above the origin. 5. Let \( x_{1}=1 \) and \( x_{n+1}=3 x_{n}-1 \) for all \( n \in \mathbb{N} \). Among the following statements, the correct one is \( \begin{array}{lll}\text { (A) }\left(x_{n}\right) \text { converges to } 3 & \text { (B) }\left(x_{n}\right) \text { converges to } 1 / 2 & \text { (C) }\left(x_{n}\right) \text { is unbounded. } \\ \text { (D) }\left(x_{n}\right) \text { is decreasing. } & \text { (E) } x_{n} \leq 10 \text { for all } n \in \mathbb{N}\end{array} \) 4. Given \( \epsilon>0 \), the statement \( x \in(1-\epsilon, 1+\epsilon) \) is equivalent to \( \begin{array}{llll}\text { (A) } x-1>-\epsilon & \text { (B) } x-1<\epsilon & \text { (C) }|x-1|>\epsilon & \text { (D) }|x-1| \leq \epsilon\end{array} \) 3. Among the following sequences, the bounded one is \( \begin{array}{llll}\text { (A) }(n) & \text { (B) }\left(\frac{n^{2}}{1+n}\right) & \text { (C) }\left(\frac{(-1)^{n} n}{1+n}\right) & \text { (D) }(-1,0,-2,0,-3,0, \ldots)\end{array} \) 2. The smallest natural number \( N \) for which \( \left|\frac{2 n+3}{n}-2\right|<\frac{1}{2} \) for all \( n \geq N \) is \( \begin{array}{llll}\text { (A) } 5 & \text { (B) } 6 & \text { (C) } 7 & \text { (D) } 8\end{array} \) Let \( h(x)=\frac{1}{4 x+1} \) and \( g(x)=\frac{1}{x} \), find \( g(h(x)) \)
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