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Home Question Bank Math Pre Calculus Archive 2025 January 11

Pre-calculus Questions from Jan 11,2025

Browse the Pre-calculus Q&A Archive for Jan 11,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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B. Un emprendedor tiene un negocio de venta de camisetas y ha observado que sus beneficios B en función del precio x de venta de cada camiseta (en dólares) pueden modelarse mediante la función: \[ \mathrm{B}(\mathrm{x})=-x^{2}+4 x+5 \] El enprendedor quiere maximizar sus beneficios y necesita saber en qué rango de precios x sus Answer all the questions below. 1.Draw the graphs representing the functions of the hyperbola on a Cartesian plane a. \( \quad 8 x y=4 \) b. \( y=3 / x \) c. \( 3 x y=12 \) d. \( y=4 / 2 x \) e. \( x y=5 \) Как изменится график функции \( g(x) = -3^x \), если мы заменим его на \( h(x) = -3^{-x} \)? Опишите отражение. \[ -2<x<7 \quad 3<y<5 \] Encadré \( \frac{1}{x}+\frac{1}{y} \) Eine Hefekultur hat zu Beginn ein Volumen von \( 2 \mathrm{~cm}^{3} \). Ihr Volumen nimmt jeden Tag um \( 15 \% \) zu. Berechne das Volumen der Hefekultur nach... \( \begin{array}{llll}\text { a) } 5 \text { Tagen, } & \text { b) } 10 \text { Tagen, } & \text { c) } 15 \text { Stunden, } & \text { d) } 40 \text { Stunden. }\end{array} \) Select all the true statements about the end behavior of the function \( f(x)=-x^{4}-5 x^{3}+5 x+3 \). - As \( x \) approaches positive infinity, \( f(x) \) approaches positive infinity - As \( x \) approaches negative infinity, \( f(x) \) approaches negative infinity - As \( x \) approaches positive infinity, \( f(x) \) approaches negative infinity - As \( x \) approaches negative infinity, \( f(x) \) approaches positive infinity 4) The range of the function \( f: f(x)=\frac{3 x^{2}-3}{x^{2}-1} \) is ............ \( \begin{array}{llll}\text { (a) } \mathbb{R}-\{1,-1\} & \text { (b) } \mathbb{R}-\{3,-3\} & \text { (c) }\{3,-3\} & \text { d) }\{3\}\end{array} \) Give the domain and range of the function. \( g(x)=(x-2)^{2}-2 \) A. Domain: all real numbers; Range: \( [-2, \infty) \) B. Domain: \( [2, \infty) \); Range: \( [-2, \infty) \) C. Domain: all real numbers; Range: \( [2, \infty) \) D. Domain: \( [-2, \infty) \); Range: all real numbers How is the graph of \( f(x)=(x-3)^{2}+7 \) generated from the graph of \( g(x)=x^{2} \) ? A. Translate \( g(x) 3 \) units right and 7 units downward to generate \( f(x) \) B. Translate \( g(x) 3 \) units right and 7 units upward to generate \( f(x) \) C. Translate \( g(x) 3 \) units left and 7 units upward to generate \( f(x) \) D. Translate \( g(x) 3 \) units left and 7 units downward to generate \( f(x) \) How is the graph of \( f(x)=(x-3)^{2}+7 \) generated from the graph of \( g(x)=x^{2} \) ? A. Translate \( g(x) 3 \) units right and 7 units downward to generate \( f(x) \) B. Translate \( g(x) 3 \) units right and 7 units upward to generate \( f(x) \) C. Translate \( g(x) 3 \) units left and 7 units upward to generate \( f(x) \) D. Translate \( g(x) 3 \) units left and 7 units downward to generate \( f(x) \)
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