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Home Question Bank Math Pre Calculus Archive 2024 December 13

Pre-calculus Questions from Dec 13,2024

Browse the Pre-calculus Q&A Archive for Dec 13,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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What is the domain of that inverse function of \( f(x)=3+\sqrt{x-2} \). a) \( [2, \infty) \) b) \( [3, \infty) \) d) \( (-\infty, 3] \) d) \( (-\infty, 2] \) A city had a population of 5,682 at the begining of 1949 and has been growing at \( 5.2 \% \) per year since then. (a) Find the size of the city at the beginning of 1976 . Answer: \( \square \) (b) During what year will the population of the city reach \( 22,586,370 \) ? Answer: Write the equation of the hyperbola \( 36 x^{2}-16 y^{2}+360 x-128 y+68=0 \) in standard form \[ \begin{array}{l}\text { Where: } \\ h=-5 \\ k=-4 \\ a=4 \\ \mathrm{a}=4)^{2} \\ b=\square\end{array} \] The rat population in a major metropolitan city is given by the formula \( n(t)=29 e^{0.01 t} \) where \( t \) is measured in years since 1994 and \( n \) is measured in thousands. (a) What was the rat population in 1994? (b) What is the rat population going to be in the year 2009? Sea \( f: R^{+} \longrightarrow R^{+} / f(x)=2 x^{2} \). ¿Es biyectiva 5. ( 0.6 ptos.) Si Carol tiene 2400 pies de cerca pa- ra cercar un corral rectangular para caballos. Las dimensiones del rectángulo que lleve al máximo el área del corral de largo y ancho son respectiva- mente: Determine each feature of the graph of the given function. \[ f(x)=\frac{3 x+14}{2 x+3} \] Answer Horizontal Asymptote: \( y=\square \) Vertical Asymptote: \( x=\square \)-Intercept: \( (\square, 0) \) No ho \( x \)-intereept \( y \)-Intercept: \( (0, \square) \) No vo \( y \)-intercept Hole: \( (\square, \square) \) No hole Find all horizontal asymptotes of the following function \[ f(x)=\frac{2(2 x+3)(x+4)}{3(x-6)(x+4)} \] Find all vertical asymptotes of the following functio \[ f(x)=\frac{4 x^{2}-1}{6 x^{2}-15 x-9} \] 2. \( y=\left\{\begin{array}{ll}1, & \text { if } 0 \leq x<3 \\ 0, & \text { if } 3 \leq x<6 \\ -1, & \text { if } 6 \leq x<9 \\ -2, & \text { if } 9 \leq x<12\end{array}\right. \)
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