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Home Question Bank Math Pre Calculus Archive 2024 December 06

Pre-calculus Questions from Dec 06,2024

Browse the Pre-calculus Q&A Archive for Dec 06,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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How are the graphs of the functions \( f(x)=\sqrt{16}^{x} \) and \( g(x)=\sqrt[3]{64}^{x} \) related? The functions \( f(x) \) and \( g(x) \) are equivalent. The function \( g(x) \) increases at a faster rate. The function \( g(x) \) has a greater initial value. The function \( g(x) \) decreases at a faster rate. What is the domain of \( f(x)=3^{x-2} ? \) \( \{x \mid x>0\} \) \( \{x \mid x<0\} \) \( \{x \mid x=0\} \) \( \{x \mid x \) is a real number \( \} \) What are the domain, range, and asymptote of \( h(x)=2^{x+4} ? \) domain: \( \{x \mid x>0\} \); range: \( \{y \mid y \) is a real number\}; asymptote: \( y=0 \) domain: \( \{x \mid x>-4\} \); range: \( \{y \mid y \) is a real number \( \} \); asymptote: \( y=-4 \) domain: \( \{x \mid x \) is a real number \( \} \); range: \( \{y \mid y>0\} \); asymptote: \( y=0 \) domain: \( \{x \mid x \) is a real number \( \} \); range: \( \{y \mid y>0\} \); asymptote: \( y=-4 \) EXERCICE 45 Soit \( \left(u_{n}\right) \) la suite numérique définie par: \( u_{0}=2 \) et pour tout \( n \in \mathbb{N}: u_{n+1}=\frac{7 u_{n}-25}{u_{n}-3} \) \( u_{0}=-\frac{1}{2} \) et pour tout \( n \in \mathbb{N}: u_{n+1}=\frac{u_{n}}{3-2 u_{1}} \) \( \begin{array}{ll}\text { 1) Démontrer par récurrence que }:(\forall n \in \mathbb{N}) u_{n} \neq 5 & \text { 1) Démontrer que : }(\forall n \in \mathbb{N}) u_{n}<0 \\ \text { 2) On pose pour tout } n \in \mathbb{N}: v_{n}=\frac{1}{u_{n}-5} . & \text { 2) Étudier la monotonie de la suite }\left(u_{n}\right) \\ \text { a) Démontrer que la suite }\left(v_{n}\right) \text { est une suite arithmé- } & \text { 3) On pose pour tout } n \in \mathbb{N}: v_{n}=\frac{u_{n}}{u_{n}-1}\end{array} \) trique. Préciser la raison et le premier terme. How are the two functions \( f(x)=0.7(6)^{x} \) and \( g(x)=0.7(6)^{-x} \) related to each other? \( g(x) \) is the reflection of \( f(x) \) over the \( x \)-axis. \( g(x) \) is the reflection of \( f(x) \) over the \( y \)-axis. \( g(x) \) is the reflection of \( f(x) \) over both axes. \( g(x) \) and \( f(x) \) will appear to be the same function. The function \( f(x)=\frac{1}{6}\left(\frac{2}{5}\right)^{x} \) is reflected across the \( y \)-axis to create the function \( g(x) \). Which ordered pair is on \( g(x) \) ? \( \left(-3, \frac{4}{375}\right) \) \( \left(-2, \frac{25}{24}\right) \) \( \left(2, \frac{2}{75}\right) \) \( \left(3,-\frac{125}{48}\right) \) Which is the range of the function \( f(x)=\frac{1}{7}(9)^{x} \) ? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0 Consider the three functions below. \( f(x)=-\frac{6}{11}\left(\frac{11}{2}\right)^{x} \quad g(x)=\frac{6}{11}\left(\frac{11}{2}\right)^{-x} \quad h(x)=-\frac{6}{11}\left(\frac{11}{2}\right)^{-x} \) Which statement is true? The range of \( h(x) \) is \( y>0 \). The domain of \( g(x) \) is \( y>0 \). The ranges of \( f(x) \) and \( h(x) \) are different from the range of \( g(x) \). The domains of \( f(x) \) and \( g(x) \) are different from the domain of \( h(x) \). Consider the exponential function \( f(x)=\frac{1}{5}\left(15^{x}\right) \). What is the value of the growth factor of the function? \( \frac{1}{5} \) \( \frac{1}{3} \) 5 15 The rat population in a major metropolitan city is given by the formula \( n(t)=58 e^{0.035 t} \) where \( t \) is measure in years since 2001 and \( n(t) \) is measured in millions. What was the rat population in 2001 (Enter answer in millions, ie: \#\#\#,\#\#\#,\#\#\#)? rats What does the model predict the rat population was in the year 2019 (Enter answer in millions, ie: \#\#\#\#\#,\#\#\#)? \( > \) Next Question
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