Topic
Q:
19. Convert the following equations from polar to rectangular form.
\( \begin{array}{lll}\text { a. } 2 \sin (\theta)+3 \cos (\theta)=\mathrm{r} & \text { b. } r=3 \csc (\theta) & \text { c. } r^{2} \sin (2 \theta)=2\end{array} \)
Q:
Graph the function.
Use the graph of \( f(x)=e^{x} \)
to obtain the graph of
\( g(x)=e^{x-4}+2 \)
Q:
Define what a logarithmic function is and provide an example.
Q:
(4 pts) Convert \( r \sin \theta-4=r^{2} \cos ^{2} \theta-4 r \cos \theta \) into a rectangular equation. S
Q:
1-Representa gudicamente a funcios:
\[ \text { a) } g(x)=\left\{\begin{array}{l}-x+2, \text { se } x<2 \\ x^{2}+1, \text { se } 2 \leqslant x<5 \\ -x+3, \text { se } x \geqslant 5\end{array}\right. \]
Q:
1- Refresenta gradicamente a funcoos:
a) \( g(x)=\left\{\begin{array}{l}-x+2 \text {, se } x<2 \\ x^{2}+1, \text { se } 2 \leqslant x<5 \\ -x+3, \text { se } x \geqslant 5\end{array}\right. \)
Q:
Express the point \( \left(9, \frac{\pi}{3}\right) \) in cartesian coordinates
Q:
4. Determine the domain of \( \frac{f}{g}(x) \); where \( f(x)=\frac{1}{x-5} \) and \( g(x)=\sqrt{x-3} \)
Q:
If \( f(x)=\sqrt{625-x^{2}} \) and \( g(x)=\sqrt{225-x^{2}} \)
what is the value of \( f(f(5))-g((g 5)) ? \)
\( f(5)=\sqrt{625}-5^{2}=16 \sqrt{6} \)
A) 0
B) 5
C) 10
D) 20
Q:
1. For the following polynomial functions, Determine the end behavior; that is,
find the power function that the graph of f resembles for large values of \( |x| \)
\( \begin{array}{ll}\text { (1) } f(x)=(x-5)^{3}(x+4)^{2} & \text { (2) } f(x)=3\left(x^{2}+8\right)\left(x^{2}+9\right)^{2}\end{array} \)
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