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Home Question Bank Math Pre Calculus Archive 2024 December 08

Pre-calculus Questions from Dec 08,2024

Browse the Pre-calculus Q&A Archive for Dec 08,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of \( f(x)=6 x^{4}-2 x^{3}-x^{2}-4 x+3 \). What is the possible number of positive real zeros? 2,0 (Use a comma to separate answers as needed.) What is the possible number of negative real zeros? (Use a comma to separate answers as needed.) Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of \( f(x)=6 x^{4}-2 x^{3}-x^{2}-4 x+3 \) What is the possible number of positive real zeros? use a comma to separate answers as needed.) Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of \( f(x)=6 x^{4}-2 x^{3}-x^{2}-4 x+3 \) What is the possible number of positive real zeros? \( \square \) (Use a comma to separate answers as needed.) \( \square \) For the function \( y=2 \log (x) \), what kind of transformation is applied? \( \square \) What is the vertical asymptote of the function \( y=\log (x+5) \) ? 7. Let \( f(x)=\frac{1}{x-1} \) and \( g(x)=\frac{2 x}{x+2} \). Find and simplify: (a) \( (f+g)(2) \) (b) \( \left(\frac{g}{f}\right)(x) \) (d) \( (f \circ g)(x) \) (c) \( (g \circ f)(2) \) Where is the function, \( h(x)=\frac{2 x-1}{x+7} \), discontinuous? \( \begin{array}{l}0.5 \\ -7 \\ -2\end{array} \) 7. The formula for the volume of a sphere is \( f(r)=\frac{4}{3} \pi r^{3} \). Determine each value. Express to the nearest tenth, if necessary. \( \begin{array}{ll}\text { a) } f(3) & \text { b) } f(10) \\ \text { c) } f\left(\frac{d}{2}\right) & \text { d) } r \text { if } f(r)=6.28\end{array} \) 5. Sin graficar, determina el dominio, recorrido \( y \) las intersecciones con los cjes de las graficas correspondientes a las siguientes funciones exponenciales. a. \( f(x)=2^{x}-1 \) b. \( h(x)=1-3^{x} \) \( h(x)=5^{x}-2 \) c. First find \( f+g, f-g, f g \), and \( \frac{f}{g} \). Then determine the domain for each function. \( f(x)=\sqrt{x+4}, g(x)=\sqrt{x-5} \) \[ \] \( (f+g)(x)=\sqrt{x+4}+\sqrt{x-5} \) What is the domain of \( f+g \) ? \( [5, \infty) \) \( (-\infty, \infty) \) \( [-4, \infty) \) ( \( f-g)(x)=\square \)
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