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Home Question Bank Math Pre Calculus Archive 2025 January 04

Pre-calculus Questions from Jan 04,2025

Browse the Pre-calculus Q&A Archive for Jan 04,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A hyperbola is represented by the equation \( \frac{x^{2}}{16}-\frac{(y-4)^{2}}{7}=1 \). Identify the asymptotes of the graph. (1 point) \( y=\frac{16}{7}(x+4) \) and \( y=-\frac{16}{7}(x+4) \) \( y=\frac{16}{7} x+4 \) and \( y=-\frac{16}{7} x+4 \) \( y=\frac{\sqrt{7}}{4} x+4 \) and \( y=-\frac{\sqrt{7}}{4} x+4 \) \( y=\frac{\sqrt{7}}{4}(x+4) \) and \( y=-\frac{\sqrt{7}}{4}(x+4) \) Which is the graph of the following equation? \( \frac{(x-3)^{2}}{4}-\frac{(y-6)^{2}}{9}=1 \) (1 point) 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). 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). 1.2 If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2 .2 \( \begin{array}{ll}1.2(x) \text { non real. } \\ 1.2 .4 & f(x) \text { undefined } \\ & f(x)>0\end{array} \) UESTION 3 re equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Shift two units to the left Shift 3 units up Shift 1 unit right and 2 units down The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) Explain how to verify if two functions are inverses of each other using compositional notation. \( n=1,2,3,4, \cdots \) \( R_{1}: 1242 \sum_{k=0}^{n=1} 1.035^{k} \) Find R\( R_{20} \) \( \left. \begin{array} { l } { n = 1,2,3,4 , \cdots } \\ { R _ { n } = 1242 \sum _ { k = 0 } ^ { n - 1 } 1.035 ^ { k } } \\ { R _ { 20 } = } \end{array} \right. \) 2 กำหนด \( r_{1}=\left\{(x, y) \in \mathbb{R} \times \mathbb{R} \mid y^{2} \leq 4-x^{2}\right\} \) และ \( r_{2}=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}|y \geq|x|\}\right. \) จงหาที้นที่ \( r_{1} \cap r_{2} \)
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