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Home Question Bank Math Pre Calculus Archive 2025 January 05

Pre-calculus Questions from Jan 05,2025

Browse the Pre-calculus Q&A Archive for Jan 05,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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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 t \( 3.1 \quad \) Shift two units to the left 3.2 Shift 3 units up 3.3 Shift 1 unit right and 2 units down 3.4 The equation of the new hyperbola has new asymptotes at \( x= \) QUESTION 4 Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g \) Clearly indicate all intercepts with the axes, turning point(s) and asympto . (ii) Use generating functions to solve the recurrence relation \( a_{n}=3 a_{n-1}+1 ; n \geq 1 \) with \( a_{0}=1 \) Or Find the domain of the function \( f(x)=\operatorname{Ln}\left(4-x^{\wedge} 2\right) \) \#1: Find the domain, range, and asymptotes for \( f(x)=\frac{x^{2}+7 x-5}{5 x^{2}-7 x-6} \) \#4: Sketch with the 4 steps \( f(x)=x^{\wedge} 3-4 x^{\wedge} 2-4 x+16 \). (20 Points) Describe the basic behavior for each at infinity based on the leading coefficient and leading exponent. (4 Points Each) \#2: \( f(x)=-5 x^{\wedge} 2+4 x \) \( \# 3: f(x)=6 x^{\wedge} 3-7 \) Problem : 1 The least value of the expression \( 2 \log _{10} x-\log _{x}(0.01) \), for \( x>1 \), is [IIT 1980 \( \begin{array}{ll}\text { (a) } 10 & \text { (b) } 2 \\ \text { (c) }-0.01 & \text { (d) None of these }\end{array} \) 4) Déterminer une valeur approchée de \( \frac{1}{\sqrt{1.0004}} \) à \( 2 \times 10^{-4} \) prés 4) Déterminer une valeur approchée de \( \frac{1}{\sqrt{1.0004}} \) à \( 2 \times 10^{-4} \) prés If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( f(x) \) non real. 1.2.3 \( f(x) \) undefined \( 1.2 .4 \quad f(x)>0 \)
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