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Home Question Bank Math Pre Calculus Archive 2024 December 27

Pre-calculus Questions from Dec 27,2024

Browse the Pre-calculus Q&A Archive for Dec 27,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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QUESTION 4 It is given that the asymptotes of \( f(x)=\frac{6}{x+p}+q \) intersect at \( (4 ; 3) \). \( 4.1 \quad \) Write down the equation of \( f \). \( 4.2 \quad \begin{array}{l}\text { Sketch the graph of } f \text {, clearly showing all the intercepts with the axes and any } \\ \text { asymptotes. }\end{array} \) \( 4.4 \quad \begin{array}{l}g \text { is one of the axes of symmetry of } f \text { and it is a decreasing function. Determine the } \\ \text { equation of } g \text {. } \\ 4.5 \\ (-3 ; 2) \text { is a point on } f \text {. Determine the coordinates of the image of this point after } \\ \text { reflection in } g \text {. }\end{array} \) (a) Montrer que \( \left(v_{n}\right) \) est une suite géométrique de raison \( \mathrm{q}=4 \) (b) Écrire \( v_{n} \) puis \( u_{n} \) en fonction de \( n \) C) Calculer en fonction de \( n: S_{n}=\sum_{k=1}^{n} v_{k} \) puis \( T_{n}=\prod_{k=1}^{n} v_{k} \) On considère la suite \( \left(u_{n}\right) \) définie par: \( u_{0}=2 e t(\forall n \in \mathbb{N}) ; u_{n+1}=\sqrt{6+u_{n}} \) 1 Montrer que : \( (\forall n \in \mathbb{N}) ; 1<u_{n}<3 \) 2 Vérifier que \( :(\forall n \in \mathbb{N}) ; 3-u_{n+1}=\frac{1}{3+\sqrt{6+u_{n}}}\left(3-u_{n}\right) \) 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 \( t=2\pi \)). j) \( \sin ^{-1}(y)+x^{3}=\sqrt{y} \) Una sucesión infinita tiene la caracteristica de que: a. El término \( a_{n} \) siempre es el último de la sucesión. b. Cada término \( a_{n} \) tiene un antecesor igual a \( a_{n+1} \) c. Cada término \( a_{n} \) es el último en sucesiones pares. d. Cada término \( a_{n} \) tiene un sucesor igual a \( a_{n+1} \) Graph, state domain and range: \[ y=-3 \sqrt{x+3}+5 \] 1. Expand \( (1+x)^{\frac{1}{3}} \) in ascending powers of x up to the term \( x^{3} \). By substituting 0.08 for \( x \) in your result. Obtain an approximation value of the cube root of 5 . 81 The range of the function \( f(x)=2-x^{2}, x \neq 0 \) is \( \ldots \ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) }]-\infty, 2] & \text { (b) }] 2, \infty[ & \text { (c) }] 0,2] & \text { (d) }[0,2]\end{array} \) Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \quad 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). Pre-Calculus 11 Practice Midterm 2 Find the \( x \)-intercepts of the following quadratic function: \( y=3 x^{2}-13 x-10 \)
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