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Home Question Bank Math Pre Calculus Archive 2024 December 29

Pre-calculus Questions from Dec 29,2024

Browse the Pre-calculus Q&A Archive for Dec 29,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Determine whether the relation \( y=\sqrt{x} \) defines \( y \) as a function of \( x \). Give the domain. Does the relation \( y=\sqrt{x} \) define \( y \) as a function of \( x \) ? A. No, because the equation \( y=\sqrt{x} \) assigns exactly one \( x \)-value to each distinct \( y \)-value. B. Yes, the equation \( y=\sqrt{x} \) assigns exactly one \( y \)-valuè to each distinct \( x \)-value in the domain. C. No, because the equation \( y=\sqrt{x} \) assigns more than one \( y \)-value to one of the \( x \)-values. D. Yes, because the equation \( y=\sqrt{x} \) assigns at least one \( y \)-value to each distinct \( x \)-value. What is the domain? \( \square \) (Type your answer in interval notation.) \( \rightarrow \) trovare Dominio, studio del segno, cascolo degle zeri \( y=\frac{x}{\sqrt{5-x}+\sqrt{x+2}} \) The domain of the function \( f: f(\mathcal{X})=\frac{1}{\sqrt{9-x^{2}}} \) is \( \begin{array}{llll}\text { (a) } \mathbb{R} & \text { (b) } \mathbb{R}-[-3,3] & \text { (c) } \mathbb{R}-\{-3,3\} & \text { (d) }]-3,3[ \end{array} \) 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 transformed as follows: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up \( 3.3 \quad \) Shift 1 unit right and 2 units down \( 3.4 \quad \) The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) 53. (ESSLCE-2013EC) What are the length \( L \) and width \( W \) of a rectangle with perimeter 10, maximize the area? A. \( L=2,500 \mathrm{~m} \) and \( W=3,000 \mathrm{~m} \) \[ \begin{array}{lll}\text { C. } L=5,000 \mathrm{~m} & \text { and } W\end{array} \] \[ \begin{array}{l}\text { B. } L=2,500 \mathrm{~m}\end{array} \] Explain how to verify if two functions are inverses of each other using compositional notation. If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real. Question 3 of 5 Identify the equations of the asymptotes. \( \frac{(x-3)^{2}}{9}-\frac{(y+3)^{2}}{16}=1 \) 5.4 - Online Quiz - Hyperbolas Question 1 of 5 Identify the center. \( \frac{x^{2}}{12}-\frac{y^{2}}{16}=1 \) write the rale of inverse function. \( f(x)=\frac{x}{\sqrt{x^{2}+1}} \)
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