Calcular la magnitud y los ángulos del siguiente vector en \( \mathrm{R}^{3} \) : \( V=2 i-4 j-3 k \)

Suppose that the function \( f \) is defined for all real numbers as follows. \[ f(x)=\left\{\begin{array}{ccc}6 & \text { if } & x<-4 \\ -10+x^{2} & \text { if } & -4 \leq x<4 \\ 2 x-2 & \text { if } & x \geq 4\end{array}\right. \] Graph the function \( f \). Then determine whether or not the function is continuous.

If \( f(x)=3^{x^{2}-4}+4 \), what is the value of \( f(-3) \), to the nearest thousandth (if necessary)?

An equation for the slant asymptote for the graph of the function \( f(x)=\frac{2 x^{2}-x+3}{x+4} \) is

\( f(x)=\frac{12 x}{7 x^{2}+9} \) Find the horizontal asymptote, if any, of the graph of the rational function. A. The horizontal asymptote is \( \square \). (Type an equation.) B. There is no horizontal asymptote.

UESTION 3 On the interval \( [-2,3] \), the maximum vertical distance between the line \( y=x+6 \) and the parabola \( y=x^{2} \) is equal to