Hallar el dominio de la siguiente función: \( f(x)=\frac{1}{\sqrt{x^{3}+2 x^{2}-3 x}} \)

Evaluate the expression. \( \log _{\sqrt{13}} 17 \approx \square \) (Type an integer or a decimal. Do not round as needed.)

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 \( (a,-b) \).

Sketch a graph of \( f \) \( f(x)=2 x-x^{2} \)

A carpenter is building a rectangular room with a fixed perimeter of 240 fit. What dimensions would yield the maximum area? Length \( (\mathrm{ft})=\square \) Width \( (\mathrm{ft})=\square \)

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