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Home Question Bank Math Pre Calculus Archive 2025 January 29

Pre-calculus Questions from Jan 29,2025

Browse the Pre-calculus Q&A Archive for Jan 29,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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The function \( f(x) \) is graphed below. What is true about the graph on the interval from \( x=-\infty \) to \( x=a \) ? The winner of the first annual Tom Morris Golf Invitational won \( \$ 180 \) in the competition which was held in 1914 . In 2015 , the winner received \( \$ 1,610,000 \). If the winner's purse continues to increase at the same interest rate, how much will the winner receive in2048? \( \begin{array}{l}\text { a. } \$ 31,472,226.82 \\ \text { b. } \$ 28,611,115.29 \\ \text { d. } \$ 29,051,286.29 \\ \text { e. } \$ 35,406,255.17 \\ \end{array} \) The sum to infinity of a convergent geometric series is 32 and \( r=\frac{1}{2} \). Find the difference between the sum to infinity and the sum of the first five terms. A specific tree grows \( 1,5 \mathrm{~m} \) in the 1 st year. Its growth each year thereafter is \( \frac{2}{3} \) of its growth in the previous year. What is the greatest height it can reach? A ball bounces \( \frac{1}{2} \) of its previous height on each bounce. Find the total Suppose Kehinde is finding an approximation to four decimal places of \( \sqrt{3} \). What is the upper bound approximation? (1 point) The graph of \( g(x)=-2 \sqrt{x+3}+1 \) is a transformation of the function \( f(x)=\sqrt{x} \). Which of the following describes the transformations applied to \( f(x) \) to obtain \( g(x) \) ? Answer Choices: - A. Reflection over the \( x \)-axis, vertical stretch by a factor of 2 , shift 3 units to the left, and shift 1 unit up - B. Reflection over the \( y \)-axis, vertical stretch by a factor of 2 , shift 3 units to the left, and shift 1 unit down - C. Reflection over the \( x \)-axis, vertical compression by a factor of 2 , shift 3 units to the right, and shift 1 unit up - D. Reflection over the \( x \)-axis, vertical stretch by a factor of 2 , shift 3 units to the right, and shift 1 unit up The function \( f(x)=\sqrt{x} \) is transformed to create \( g(x)=-\sqrt{x-3}+5 \). Which of the following describes the transformations applied to \( f(x) \) to obtain \( g(x) \) ? Answer Choices: - A. Reflection over the \( x \)-axis, shift 3 units to the right, and shift 5 units down - B. Reflection over the \( x \)-axis, shift 3 units to the right, and shift 5 units up - C. Reflection over the \( y \)-axis, shift 3 units to the left, and shift 5 units up - D. Reflection over the \( x \)-axis, shift 3 units to the left, and shift 5 units up The graph of \( g(x)=-2 \sqrt{x+3}+1 \) is a transformation of the function \( f(x)=\sqrt{x} \). Which of the following describes the transformations applied to \( f(x) \) to obtain \( g(x) \) ? Answer Choices: - A. Reflection over the \( x \)-axis, vertical stretch by a factor of 2 , shift 3 units to the left, and shift 1 unit up - B. Reflection over the \( y \)-axis, vertical stretch by a factor of 2 , shift 3 units to the left, and shift 1 unit down C. Reflection over the \( x \)-axis, vertical compression by a factor of 2 , shift 3 units to the right, and shift 1 unit up - D. Reflection over the \( x \)-axis, vertical stretch by a factor of 2 , shift 3 units to the right, and shift 1 unit up The function \( f(x)=\sqrt{x} \) is transformed to create \( g(x)=-\sqrt{x-3}+5 \). Which of the following describes the transformations applied to \( f(x) \) to obtain \( g(x) \) ? Answer Choices: A. Reflection over the \( x \)-axis, shift 3 units to the right, and shift 5 units down - B. Reflection over the \( x \)-axis, shift 3 units to the right, and shift 5 units up - C. Reflection over the \( y \)-axis, shift 3 units to the left, and shift 5 units up - D. Reflection over the \( x \)-axis, shift 3 units to the left, and shift 5 units up B) On considère les fonctions f et g définies par: \( f(x)=-2 x^{2}+1 \) et \( g(x)=\sqrt{1+x} \) 1) Déterminer l'ensemble de définition de gof 2) Déterminer l'ensemble de définition de fOg 3) Expliciter \( f 0 g(x) \) et gof \( (x) \). 4) On donne \( h(x)=\sqrt{x^{2}-3 x+2} \) et \( k(x)=\sqrt{1-x^{2}} \) : Déterminer ie du aaine de définition de koh. B) On considère les fonctions f et g définies par: \( f(x)=-2 x^{2}+1 \) et \( g(x)=\sqrt{1+x} \) 1) Déterminer l'ensemble de définition de gof 2) Déterminer l'ensemble de définition de fOg 3) Expliciter \( f 0 g(x) \) et gof \( (x) \). 4) On donne \( h(x)=\sqrt{x^{2}-3 x+2} \) et \( k(x)=\sqrt{1-x^{2}} \) : Déterminer ie du aaine de définition de koh.
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