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Home Question Bank Math Pre Calculus Archive 2025 January 15

Pre-calculus Questions from Jan 15,2025

Browse the Pre-calculus Q&A Archive for Jan 15,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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2.28 \( \sqrt{\frac{1}{x}+\frac{2}{x-1}}+\sqrt{7-x} \quad\left|0<x \leq \frac{1}{3}, 1<x \leq 7\right| \) 13 Compare les nombres réels suivants \( \begin{array}{ll}\text { 1. } \ln 7 \text { et } \ln 5 ; & 2 \cdot \ln \sqrt{3} \text { et } \ln \frac{1}{2} \\ \text { 3. } \ln 29 \text { et } \ln 4 \sqrt{5}\end{array} \) 13. Compare les nombres réels suivants: \( \begin{array}{ll}\ln 7 \text { et } \ln 5 ; & 2 \cdot \ln \sqrt{3} \text { et } \ln \frac{1}{2}\end{array} \) While using a table of values to estimate the value of \( x \) where \( f(x)=g(x) \), you see that there are three sign changes in the \( f(x)-g(x) \) column. How many possible solutions for \( x \) are there? If there are three sign changes in the \( f(x)-g(x) \) column, there will be \( \square \) possible solutions Points possible: 1 Allowed attompte: 2 Check Answer \[ f(x)=\frac{6}{x-2}+3 \] Write down the equations of the asymptotes of the graph of \( f \). White down the domain of \( f \). Drsw a sketch graph of \( f \) in your ANSWER BOOK, indicating the intercept(s) wi the aves and the syymptotes. The graph of \( f \) is translated to \( g \). Describe the tramsformation in the fo \( (x ; y) \rightarrow \) If the axes of symmetry of \( g \) are \( y=x+3 \) and \( y=-x+1 \). QUESTION 5 Consider the function \( f(x)=\frac{3}{x-1}-2 \). Write down the equations of the asymptotes of \( f \). 3 Calculate the intercepts of the graph of \( f \) with the axes. Sketch the graph of \( f \) on DIAGRAM SHEET I. 4 Write down the range of \( y=-f(x) \). Describe, in words, the transformation of \( f \) to \( g \) if \( g(x)=\frac{-3}{x+1}-2 \). 4 QUESTION 5 Consider the function \( f(x)=\frac{3}{x-1}-2 \) 5.1 Write down the equations of the asymptotes of \( f \). 5.2 Calculate the intercepts of the graph of \( f \) with the axes. 5.3 Sketch the graph of \( f \) on DIAGRAM SHEET I .4 Write down the range of \( y=-f(x) \) Describe, in words, the transformation of \( f \) to \( g \) if \( g(x)=\frac{-3}{x+1}-2 \) 5 Let \( \stackrel{\rightharpoonup}{\mathbf{v}} \) be the vector with initial point \( (2,5) \) and terminal point \( (8,13) \), and let \( \stackrel{\rightharpoonup}{\mathbf{w}}=\langle-2,4\rangle \). a. Express \( \stackrel{\rightharpoonup}{\mathbf{v}} \) in component form and find \( \|\stackrel{\rightharpoonup}{\mathbf{v}}\| \). Then, using algebra, find b. \( \stackrel{\rightharpoonup}{\mathbf{v}}+\stackrel{\mathbf{w}}{ } \) c. \( 3 \stackrel{\rightharpoonup}{\mathbf{v}} \), and d. \( \stackrel{\rightharpoonup}{\mathbf{v}}-2 \stackrel{\rightharpoonup}{\mathbf{w}} \). Consider the function \( g(x)=\log (x+1) \). The domain of \( g \) is the interval from negative one to infinity \( \quad \), and the \( x \)-intercept is 1 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 \( f(x)>0 \)
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