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Home Question Bank Math Pre Calculus Archive 2024 December 25

Pre-calculus Questions from Dec 25,2024

Browse the Pre-calculus Q&A Archive for Dec 25,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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The population of a town is currently 20,000 and is growing at a rate of 5% per year. Write an exponential function that models the population growth over time. \( f ( x ) = x + \frac { 1 } { x } \rightarrow f ( 1 ) , f ( - 1 ) , f ( 2 ) , f ( \frac { 1 } { 2 } ) \) 1. \( f(x)=x+\frac{1}{x} \rightarrow f(1), f(-1), f(2), f\left(\frac{1}{2}\right) \) \( f ( x ) = x + \frac { 1 } { x } \rightarrow f ( 1 ) , f ( - 1 ) , f ( 2 ) , f ( \frac { 1 } { 2 } ) \) यदि \( g(x) = 2^{x} \), तो इसके इनवर्स फ़ंक्शन की पहचान करें और उसका डोमेन तथा रेंज लिखिए। 10) If \( f(x)=\frac{1}{x-a}+b \), then \( f^{-1}(a)+f(b)= \) (d) \( \sqrt{1+x^{2}} \) 2. Постройте график функции: \( \begin{array}{ll}\text { a) } y=\sqrt{x-1}-1 ; & \text { в) } y=-4(x-2)^{2}-1 \\ \text { б) } y=\frac{4}{x-5}-1 ; & \end{array} \) I. Work Out (Show the necessary steps) For the rational functions (a-d) given below answer question (i-vi) each of the following i. Find the domain ii. \( \quad \) Find hole, if any iii. Find the vertical asymptote(s), if any iv. Find the horizontal or oblique asymptote, if any v. Find the \( x \)-intercept(s) and \( y \) - intercept(s) vi. \( \quad \) Prepare sign chart vii. Sketch the graph of each rational function a. \( \quad f(x)=\frac{x+2}{x^{2}-9} \) The population of a certain species in a protected area can be modeled by the function \( P(t) = 200 + 50 \sin(t) \), where \( t \) is measured in years. Determine the total population increase over one complete cycle (from \( t=0 \) to \( t=2\pi \)).
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