Pre Calculus Questions & Answers

Rango Dominio \( \operatorname{cog}\left(\operatorname{sen}^{-1} x\right)=\sqrt{1-x^{2}} \)

What is the direction of the vector defined by <5, \( 12> \) ? Give your answer in degrees rounded to the nearest tenth.

What is the magnitude of the vector defined by \( <5,12>? \)

Let \( f(x)=\frac{1}{x-4} \) and \( g(x)=\frac{5}{x}+4 \) Then \( (f \circ g)(x)=\square \) \( (g \circ f)(x)=\square \)

Use the properties of logarithms to evaluate each of the following expressions. \( \begin{array}{l}\text { (a) } 4 \ln ^{2}+\ln e^{9}=\square \\ \text { (b) } \log _{2} 5-\log _{2} 20=\square\end{array} \)

2. Determinantni hisoblang. \( \left|\begin{array}{cccc}8 & -7 & 6 & 1 \\ 3 & 5 & -1 & 4 \\ 0 & 3 & 2 & -3 \\ -1 & 0 & 3 & -2\end{array}\right| \)

2. Determinantni hisoblang. \( \left|\begin{array}{cccc}8 & -7 & 6 & 1 \\ 3 & 5 & -1 & 4 \\ 0 & 3 & 2 & -3 \\ -1 & 0 & 3 & -2\end{array}\right| \)

9. Para las siguientes funciones paramétricas: \( \begin{array}{l}\text { a) Bosquejar el gráfico. } \\ \text { b) Eliminar el parámetro y hallar la ecuación cartesiana. } \\ \begin{array}{ll}x=1-t^{2} & x=\sqrt{t} \\ y=t-2 & y=1-t \\ -2 \leq t \leq 2 & 0 \leq t \leq 16\end{array}\end{array} \).

Graph the piecewise-defined function. \( f(x)=\left\{\begin{aligned} x-2 & \text { if } x \leq-2 \\ -4 & \text { if } x>-2\end{aligned}\right. \)

Using visual observation, determine whether the graph is symmetric with respect to the (a) \( x \)-axis, (b) \( y \)-axis, or \( (\mathrm{c}) \) the origin. (a) Is the graph symmetric with respect to the \( x \)-axis? Choose the correct answer below. A. No, because for \( \left(\frac{\pi}{4}, 4\right) \), the point \( \left(-\frac{\pi}{4}, 4\right) \) is not on the graph. B. No, because for \( \left(\frac{\pi}{4}, 4\right) \), the point \( \left(\frac{\pi}{4},-4\right) \) is not on the graph. C. Yes, because if \( (a, b) \) is on the graph, then so is \( (-a, b) \). D. Yes, because if \( (a, b) \) is on the graph, then so is \( (a,-b) \). (b) Is the graph symmetric with respect to the \( y \)-axis? Choose the correct answer below. A. Yes, because if \( (a, b) \) is on the graph, then so is \( (-a, b) \). Because for \( \left(\frac{\pi}{4}, 4\right) \), the point \( \left(-\frac{\pi}{4}, 4\right) \) is not on the graph. C. No, because for \( \left(\frac{\pi}{4}, 4\right) \), the point \( \left(\frac{\pi}{4},-4\right) \) is not on the graph. (c) Is the graph symmetric with respect to the origin? Choose the correct answer below. A. Yes, because if \( (a, b) \) is on the graph, then so is \( (-a, b) \). B. Yes, because if \( (a, b) \) is on the graph, then so is \( (-a,-b) \). B C. Yes, because if \( (a, b) \) is on the graph, then so is \( (a,-b) \).