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Home Question Bank Math Pre Calculus Archive 2025 January 20

Pre-calculus Questions from Jan 20,2025

Browse the Pre-calculus Q&A Archive for Jan 20,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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At the end of 2010 , a shopping website had 100,000 users. The number of users grew at a rate of \( 30 \% \) per year until the end of 2015 . How many more users joined the website between the end of 2012 and the end of 2015 ? Graph each of the following functions. \( \begin{array}{ll}\text { a. } n(x)=-4(0.5)^{x}-3 & \text { b. } m(x)=2 \log _{3}(x-2)+1\end{array} \) ach statement describes a transformation of the graph of \( f(x)=x^{2} \). Which statement correctly describes the graph of the function hown below? \[ g(x)=3(x-6)^{2}-4 \] A. It is the graph of \( f(x)=x^{2} \) vertically compressed, and then translated 6 units down and 4 units to the left. B. It is the graph of \( f(x)=x^{2} \) vertically stretched, and then translated 4 units down and 6 units to the right. C. It is the graph of \( f(x)=x^{2} \) vertically compressed, and then translated 4 units down and 6 units to the left. D. It is the graph of \( f(x)=x^{2} \) vertically stretched, and then translated 6 units down and 4 units to the right. c) Draw the function \( f(x)=1-3 x+x^{2} \) where \( x \in[-1,4] \), then find: \( \begin{array}{ll}\text { i) the vertex of the curve } & \text { ii) max. point of } f(x) \\ \text { iii) equation of axis of symmetry. }\end{array} \) Given: \( k(x)=-2 \sqrt{\frac{1}{3}(x+5)}-4 \) The pressure of a fluid flowing through a closed system, \( P \), after \( t \) seconds can be modeled by the function \( P(t)=100+30 \sin \left(\frac{12 \pi}{5} t\right) \). Answer parts (a) through (c) below. (a) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 100 mmHg . The solution set is \( \{0,0.42,0,83\} \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) (b) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 130 mmHg . The solution set is \( \{0.21\} \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) (c) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is between 100 and 105 mmHg . (Use ascending order. Type an integer or decimal rounded to two decimal places as needed.) A. \( \square . \square \) B. \( \square, \square][\square . \square \) C. \( \square \square \square \square \square \square \square \square . \square \) The pressure of a fluid flowing through a closed system, \( P \), after \( t \) seconds can be modeled by the function \( P(t)=100+30 \sin \left(\frac{12 \pi}{5} t\right) \). Answer parts (a) through (c) below. (a) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 100 mmHg . The solution set is \( \{\square\} \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) [0/1 Points] DETAILS MY NOTES OSCAT2 3.2.057. Suppose the range of a function \( f \) is \( [-2,9] \). What is the range of \( |f(x)| \) ? (Enter your answer using interval notation.) PREVIOUS ANSWER 2) Vertical-line test - Draw a picture of an absolute value function and draw an example that shows it passes the vertical line test \begin{tabular}{l} Given: \( h(x)=\frac{2}{x+3}-1 \) \\ 4.1 Write down the equations of the asymptotes of \( h \). \\ \hline\end{tabular}
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