Precálculo preguntas y respuestas

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 \( (a,-b) \).

1. \( 25 x^{2}+y^{2}-200 x+6 y+384=0 \), centro 2. \( (x+1)^{2}+(y+8)^{2}=100 \), intersecciones con el eje \( x \) 3. \( y^{2}-(x-2)^{2}=1 \), intersecciones con el eje \( y \) 4. \( y^{2}-y+3 x=3 \), pendiente de la recta tangente en \( (1,1) \) 5. \( x=t^{3}, y=4 t^{3} \), nombre de la gráfica rectangular 6. \( x=t^{2}-1, y=t^{3}+t+1 \), intersecciones con el eje \( y \) 7. \( r=-2 \cos \theta \), nombre de la gráfica polar 8. \( r=2+\operatorname{sen} \theta \), nombre de la gráfica polar 19. \( r=\operatorname{sen} 3 \theta, \operatorname{tangentes~a~la~gráfica~en~el~origen~} \) 20. \( r=\frac{1}{2+5 \operatorname{sen} \theta} \), excentricidad 21. \( r=\frac{10}{1-\operatorname{sen} \theta} \), foco yértice 22. \( r=\frac{12}{2+\cos \theta} \), centro

Empic ta aproximacion para C) \( \sqrt{102}+\sqrt[4]{80} \)

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

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 \( (\mathrm{ft})=\square \)

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

Sketch the segment \( r=\sec \theta \) for \( 0 \leq \theta \leq \frac{\pi}{9} \). Then compute its length in two ways: as an integral in pola coordinates and using trigonometry.

La altura, \( h \), de un globo de aire caliente puede modelarse con la función polinómica \( h(t) = -4t^{2} + 64t + 16 \), donde \( t \) es el tiempo en segundos. ¿Cuánto tiempo tardará en alcanzar su altura máxima?