1- Refresenta gradicamente a funcoos: a) \( g(x)=\left\{\begin{array}{l}-x+2 \text {, se } x<2 \\ x^{2}+1, \text { se } 2 \leqslant x<5 \\ -x+3, \text { se } x \geqslant 5\end{array}\right. \)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (-7,0) \) and \( (7,0) \); vertices at \( (3,0) \) and \( (-3,0) \)

2- Work out composite functions \( f \circ g \) and \( g \circ f \) for each of the following pairs of functions. \( \begin{array}{ll}\text { (a) } f(x)=x-1 \text { and } g(x)=x^{3} & \text { (b) } f(x)=\sqrt{x} \text { and } g(x)=x-2\end{array} \)

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ -3 \sqrt{3}+3 i \] \( -3 \sqrt{3}+3 i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \) (Type the value for \( r \) as an exact answer, using radicals as needed. Type the value for \( \theta \) as an intege as needed.)

Suppose the half-life of a drug in the bloodstream is 9 hours. To the nearest milligram, how much of the drug is left in the bloodstream 20 hours after a 260 milligram dose? 56 milligrams 32 milligrams 190 milligrams 117 milligrams

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-3} \) Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote.