Sketch a graph of the function. Use transformations of functions when ever possible. f(x)=sqrt[3]{-x}

Standard transformations can be used to help graph rational functions of the form ${\displaystyle f\left(x\right)=\frac{A}{Bx-C}+D}$ Explain how the parameters A, B, C, and D relate to the graph of the rational functions.

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations.
${\displaystyle y=2\sqrt{x+1}}$

Find the volume of the solid generated by revolving the shaded region

For each of the following functions f (x) and g(x), express g(x) in the form ${\displaystyle a:f(x+b)+c}$ for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map ${\displaystyle f\left(x\right)\to g\left(x\right).\left(a\right)\left(i\right)}$
${\displaystyle f\left(x\right)=x^2,g\left(x\right)=2x^2+4x}$
${\displaystyle \left(ii\right)f\left(x\right)=x^2,g\left(x\right)=3x^2-24x+8}$
${\displaystyle \left(b\right)\left(i\right)f\left(x\right)=x^2+3,g\left(x\right)=x^2-6x+8}$
${\displaystyle \left(ii\right)f\left(x\right)=x^2-2,g\left(x\right)=2+8x-4x^2}$

Begin by graphing
${\displaystyle f\left(x\right)={\log }_{2}x}$
Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function s domain and range.
${\displaystyle g\left(x\right)=\frac{1}{2}{\log }_{2}x}$

Find the area of the shaded region

For the function f whose graph is given, state the following.

(a) $\underset{x\to \mathrm{\infty }}{lim}f(x)$
b) $\underset{x\to -\mathrm{\infty }}{lim}f(x)$
(c) $\underset{x\to 1}{lim}f(x)$
(d) $\underset{x\to 3}{lim}f(x)$
(e) the equations of the asymptotes
Vertical:- ?
Horizontal:-?