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Home Question Bank Math Pre Calculus Archive 2024 November 13

Pre-calculus Questions from Nov 13,2024

Browse the Pre-calculus Q&A Archive for Nov 13,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Finding a final amount in a word problem on exponentinl growth or decay The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 135 grams of a radioactive isotope, how much will be left after 3 half-lives? Use the calculator provided and round your answer to the nearest gram. The radioactive substance uranium- 240 has a half-life of 14 hours. The amount \( A(t) \) of a sample of uranium- 240 remaining (in grams) after \( t \) hours is given by the following exponential function. \[ A(t)=5600\left(\frac{1}{2}\right)^{\frac{t}{14}} \] Find the amount of the sample remaining after 11 hours and after 40 hours. Round your answers to the nearest gram as necessary. Question 14 (1 point) Given the function \( f(x)=\sqrt{x-h}+k \) with a domain of \( \{x \mid x \geq-5, x \in R\} \) and a range of \( \{y \mid y \geq 8, y \in R\} \), which of the following best describes the vertical and horizontal translations with respect to the graph of \( f(x)=\sqrt{x} \) ? 5 units to left and 8 units up 8 units to left and 5 units down to left and 5 units up 5 units to left and 8 units down Question 15 (1 point) Question 9 (1 point) Compared to the graph of \( f(x)=\sqrt{x+2} \), the graph \( g(x)=\sqrt{2-x} \) is a A) reflection in the \( x \) - and \( y \)-axes B) reflection in the \( x \)-axis Question 8 (1 point) Which choice best describes the combination of transformations that mus applied to the graph of \( f(x)=\sqrt{x} \) to obtain the graph of \( g(x)=2 \sqrt{x-4} \) ? Question 7 (1 point) Compared to the graph of the function \( f(x)=\frac{1}{x} \), the graph of the function \( g(x)=\frac{1}{x-1} \) is translated A) 1 unit up B) 1 unit to the right C) 1 unit down D) 1 unit to the left (1) EJercitación. Trazar la gráfica de cada funcion. Determinar su dominio y su rango es creciente, decreciente y constante. \( \begin{array}{ll}\text { 1. } f(x)=\left\{\begin{array}{ll}x+1 & \text { si } x>0 \\ -2 x-3 & \text { si } x \leq 0\end{array}\right. \\ \text { 4. } f(x)=\left\{\begin{array}{ll}x+2 & \text { si } x<-1 \\ x+4 & \text { si } x>-1 \\ x^{2} & \text { si } x>1 \\ x^{3} & \text { si } x \leq 1\end{array}\right. \\ \begin{array}{ll}x+2 & \text { si } x=-1\end{array} & \text { 5. } f(x)=\left\{\begin{array}{ll}(x-1)^{2} & \text { si } x>2 \\ x+2 & \text { si } x \leq 2\end{array}\right.\end{array} \) (4 of 10) The graph \( f(x) \) is transformed by the following sequence. 1. Shift right 5 units 2. Reflect over \( y \)-axis 3. Shift down 8 units \( \begin{array}{l}y=-f(x-5)-8 \\ y=-f(x+5)-8 \\ y=f(-x+5)-8 \\ \text { Which is an equation for the new graph? } \\ \begin{array}{l}y \\ y\end{array}\end{array} \) HALLAR EL DOMINIO DE \( F(x)=\sqrt{L N(x-S)} \) 13. Dada la función \( f(x)=\log _{2} x \) Sin utilizar tablas de valores dibuja las funciones: \( g(x)=3+\log _{2} x \) \( h(x)=-1+\log _{2} x \) \( m(x)=\log _{2}(x+2) \) \( f(x)=\log _{2}(x-4) \)
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