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Home Question Bank Math Pre Calculus Archive 2025 January 03

Pre-calculus Questions from Jan 03,2025

Browse the Pre-calculus Q&A Archive for Jan 03,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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3. Realiza la gráfica de una función \( f \) cuyo dominio sè todo el conjunto de los números reales y que satisfa ga las siguientes condiciones en cada caso: - fes una función par. - fes creciente en \( [0,2] \) y decreciente en \( (2,8) \). - \( f(2)=3 \). Eéterminer \( g \) et \( h \) lorsqué 5 : Soit la fonction paire \( f \) définie sur \( [-3 ; 3] \) telle que pour tout réel \( x \) de l'intervalle \( [0 ; 3] \) on ait \( f(x)=x+1 \) 1) Définir \( f \) pour \( x \in[-3 ; 0[ \) 2) Tracer la courbe représentative de la fonction \( f \). 3) Peut-on répondre aux mémes questions sif \( f \) est impaire? 3.3 The following sequence forms a convergent geometric sequence: \( \frac{3}{(x-1)^{2}}+\frac{1}{(x-1)}+\frac{1}{3}+\frac{(x-1)}{9}+\ldots \) 3.3.1 Determine the possible values of x . QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up \( 3.3 \quad \) Shift 1 unit right and 2 units down \( 3.4 \quad \) The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) QUESTION 4 Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). Solve the equation to four decimal places. \( e^{x}=3.329 \) The solution is \( x \approx \square \). (Round to four decimal places.) Question 3 of 10 This quiz: 100 point(s) possible This question: 10 point(s) possible Describe verbally the transformations that can be used to obtain the graph of g from the graph of f \[ g(x)=7^{x-6} \cdot f(x)=T^{x} \] Exercice 3 : Pour chacune des fonctions numériques définies ci-dessous, préciser l'ensemble de définition suivant les valeurs du paramètre réel m. \( f(x)=\frac{3}{|x|+m} ; f(x)=\sqrt{x^{2}+m} ; f(x)=\frac{x^{2}-16}{x^{2}-m x+1} ; f(x)=\sqrt{x^{2}-m x+1} \) (a) Without using a calculator, determine positive integers \( m \) and \( n \) for which \[ \sin ^{6} 1^{\circ}+\sin ^{6} 2^{\circ}+\sin ^{6} 3^{\circ}+\cdots+\sin ^{6} 87^{\circ}+\sin ^{6} 88^{\circ}+\sin ^{6} 89^{\circ}=\frac{m}{n} \] (The sum on the left side of the equation consists of 89 terms of the form \( \sin ^{6} x^{\circ} \), where \( x \) takes each positive integer value from 1 to 89 .) (b) Let \( f(n) \) be the number of positive integers that have exactly \( n \) digits and whose digits have a sum of 5 . Determine, with proof, how many of the 2014 integers \( f(1), f(2), \ldots, f(2014) \) have a units digit of 1 . If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real.
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