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Home Question Bank Math Pre Calculus Archive 2025 January 18

Pre-calculus Questions from Jan 18,2025

Browse the Pre-calculus Q&A Archive for Jan 18,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( f(x)=\frac{1}{x-3}, g(x)=\frac{3 x+1}{x} \) A. Use composition to prove whether or not the functions are Inverses of each other. B. Express the domain of the compositions using interval notation. Follow the steps for graphing a rational function to graph the function \( R(x)=\frac{x^{2}}{x^{2}+x-20} \) . Ine runcuon nas unree verucal asymprotes. I ne rermost asympiote is the miadie asympiote is and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote Determine the behavior of the graph on either side of any vertical asymptotes, if one exisis. Select the correct choice below and, if necessary, fillin the answer box (es) within your choice. A. It approaches \( \infty \) on one side of the asymptote(s) at \( x=\square \) and \( -\infty \) on the other It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) I (Type integers or simplified fractions Use a comma to separate answers as needed Type each answer only once.) B. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and - \( \infty \) on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( \mathrm{x}= \) \( \square \) . (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no vertical asymptote. Follow the steps for graphing a rational function to graph the function \( P(x)=\frac{x^{4}+x^{2}+10}{x^{2}-100} \). I ne runction nas inree vericar asymptotes. I ne reimost asymptote is \( \qquad \) the miaale asymptote is and the rightmost asymptote is \( \square \) (Type equations. Use integers or fractions for any numbers in the equations.) D. The function has no vertical asymptole. Determine the behavior of the graph on either side of any vertical asymptates, if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. It approaches \( \infty \) on one side of the asymptote(s) at \( x=\square \) and \( -\infty \) on the other. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and \( -\infty \) on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. The function has no vertical asymptote. Follow the steps for graphing a rational function to graph the function \( P(x)=\frac{x^{4}+x^{2}+10}{x^{2}-100} \) Ine tunction nas three vertical asympiotes ine retmost asymptote is The miogie asympioie is and the rightmost asymptote is \( \square \) (Type equations Use integers or fractions for any numbers in the equations.) D. The function has no vertical asymptote Determine the behavior of the graph on eitherside of any vertical asymptotes, if one exists. Select the correct choice below and if necessary, fill in the answer box(es) to eomplete your choice. A. It approaches \( \infty \) on one side of the asymptote(s) at \( x=\square \) and \( -\infty \) on the other. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) जोType integers or simplified fractions Use a comma to separate answers as needed. Type each answer only ance.) B. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and \( -\infty \) on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptotes \( (\mathrm{s}) \) at \( \mathrm{x}= \) \( \square \) \( \square \). (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. The function has no vertical asymptote. Follow the steps for grapting a rational function to graph the function \( \rho(x)=\frac{x^{4}+x^{2}+10}{x^{2}-100} \) anly once.) C. The graph will cross the x -axis at \( \mathrm{x}= \) (Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once.) D. There is no \( x \)-intercept. Determine the vertical asymptote(s), it one exisis Select the correct choice below and if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptole, \( \square \) (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two verfical asymptotes The leftmost asymptote is \( \square \) , and the rightmost asymptote is \( \square \) . (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has three vertical asymptotes. The leftmost asymptate is \( \square \) the middle asymptote is and the rightmost asymptote is \( \square \) (Type equations. Use integers or fractions for any numbers in the equations.) D. The function has no vertical asymptote. Follow the steps for graphing a rational function to graph the function \( P(x)=\frac{x^{4}+x^{2}+10}{x^{2}-100} \). Write \( \mathrm{P}(\mathrm{x}) \) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete yo choice. A. \( P(x)= \) \( \square \) (Simplity your answer:) B. \( P(x) \) is already in lowest terms. Locate the intercept(s) of the graph. Select the corfect cholee below and, if necessary, fill in the answer box(es) to complete your choice. A. The graph has \( x \)-intercept(s) \( \square \) and y intercept \( \square \) (Simplify your answers Type integers orfractions Use a comma to separate answers as needed. Type each answer only once) B. The graph has \( x \)-intercept(s) \( \square \) and no \( y \)-intercept. (Simplify your answer Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) C. The graph has \( y \)-intercept \( \square \) and no \( x \)-intercept. (Simplify your answer, Type an integer or a fraction.) D. The graph has neither \( x \)-intercepts nor \( y \)-intercepts. Descrivi come si comporta graficamente la funzione \( g(x) = \sqrt{2x-5} \) rispetto agli assi cartesiani. Follow the steps for graphing a rational function to graph the function \( P(x)=\frac{x^{4}+x^{2}+2}{x^{2}-1} \). How the steps for graphing a rational function to graph the function \( P(x)=\frac{x^{4}+x^{2}+4}{x^{2}-4} \) Ine runcton nas unree verical asymptotes ine termost asymprote is the miarie asym and the rightmost asymptote is (Type equations Use integers or-fractions for any numbers in the equations.) D. The function has no vertical asymptote etermine the behavior of the graph on either side of any vertical asymptotes, if one exists. Select t hoice below and, if necessary, fill in the answerbox(es) to complete your choice. A. It approaches \( \infty \) on one side of the asymptote(s) at \( x=\square \) and \( -\infty \) on the other It approac or \( -\infty \) on both sides of the asymptote(s) at \( \bar{x}= \) \( \square \) (Type integers or simplified fractions Use a comma to separate answers as needed Type ee only once.) B. It approaches either \( \infty \) or \( -\infty \) on both sides of the asymptote(s) at \( x= \) \( \square \) (Type an integer or a simplified fraction Use a comma to separate answers as needed. Type only once.) C. It approaches \( \infty \) on one side of the asymptote(s) at \( x= \) \( \square \) and \( -\infty \) on the other. Follow the steps for graphing a rational function to graph the function \( P(x)=\frac{x^{4}+x^{2}+4}{x^{2}-4} \) only once.) C. The graph will cross the x-axis at \( x \) - (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Typ only once.) Determine the vertical asymptote(s), if one ex-intercept. answer box(es) to complete your-choice. Select the correct choice below and, if necessary, A. The function has one vertical asymptote, \( \square \). (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \( \square \), and the rightmost as (Type equations Use integers or fractions for any numbers in the equations ) C. The function has three vertical asymptotes. The leftmost asymptote is \( \square \), the middle asympte and the rightmost asymptote is \( \square \).
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