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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 the given function to complete parts a) through e) below. \( f(x)=-x^{4}+25 x^{2} \) a) Use the Leading Coefficient Test to determine the graph's end behavior. A. The graph of \( f(x) \) rises left and rises right. B. The graph of \( f(x) \) rises left and falls right. C. The graph of \( f(x) \) falls left and rises right. D. The graph of \( f(x) \) falls left and falls right. Determine each feature of the graph of the given function. \[ f(x)=\frac{5 x-5}{3 x^{2}-5 x+2} \] Answer Horizontal Asymptote: \( y=\square \) Nertical Asymptote: \( x=\square \) No horizontal asmptote \( x \)-Intercept: \( (\square, 0) \) No \( x \)-intererept \( y \)-Intercept: \( (0, \square) \) No \( y \)-intereept Hole: \( (\square, \square) \) No hole Find all horizontal asymptotes of the following function. \[ f(x)=\frac{5 x^{2}-17 x-12}{10 x+6} \] Halle el dominio y rango de la función: \( f(x)=\left|2 x^{2}-8 x\right|-8 \) Express the sum using summation notation. Use 1 as the lower limit of summation and \( i \) for the index of summation. \( \frac{1}{3}+\frac{2}{4}+\frac{3}{5}+\cdots+\frac{12}{12+2} \) \( \frac{1}{3}+\frac{2}{4}+\frac{3}{5}+\cdots+\frac{12}{12+2}= \) Question Which of the following exponential functions is increasing (from left to right)? Select two correct answers. Select all that apply: \( \square f(x)=(3.2)^{x} \) \( f(x)=\left(\frac{1}{5}\right)^{x} \) \( \square f(x)=(2.2)^{x} \) \( \square f(x)=(0.12)^{x} \) CONTEXTO: Este tipo de pregunta se desarrolla en torno a un (1) ENUNCIADO y cuatro (4) opciones de respuesta (A. B, Cy D). Sólo una (1) de estas opciones responde correctamente a la pregunta. ENUNCIADO: Se tiene una hipérbola con centro en el origen; la constante a=4 y la constante b=3, podemos decir que la ecuación canónica que representa a la hipérbola es: NOTA: recuerde que la ecuación canónica de la hipérbola centrada en C(h,k) con eje focal horizontal está determinada por la expresión \( \frac{(x=h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 \) a. \( \frac{x^{2}}{4}-\frac{y^{2}}{3}=1 \) b. \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=1 \) c. \( \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 \) d. \( \frac{x^{2}}{\sqrt{4}}-\frac{y^{2}}{\sqrt{3}}=1 \) Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros of \( f(x)=x^{3}+3 x^{2}+8 x+7 \). What are the possible numbers of positive real zeros? 0 (Use a comma to separate answers as needed.) What are the possible numbers of negative real zeros? (Use a comma to separate answers as needed.) Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros of \( f(x)=x^{3}+3 x^{2}+8 x+7 \). 2 What are the possible numbers of positive real zeros? 0 (Use a comma to separate answers as needed.) What are the possible numbers of negative real zeros? \( \square \) (Use a comma to separate answers as needed.) Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros of \( f(x)=x^{3}+3 x^{2}+8 x+7 \). \( \square \) (Use a comma to separate answers as needed.) What are the possible numbers of positive real zeros?
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