Sketch a graph of the function. Use transformations of functions when ever possible. f(x)= frac{1}{(x - 1)^{3}}

h is related to one of the six parent functions.
a) Identify the parent function f.
b) Describe the sequence of transformations from f to h.
c) Sketch the graph of h by hand.
d) Use function notation to write h in terms of the parent function f.
${\displaystyle h\left(x\right)={(-x)}^2-8}$

${\displaystyle f\left(x\right)=9,\text{if}x\le -4,\text{and}f\left(x\right)=ax+b,\text{if}-4<x<5,\text{and}f\left(x\right)=-9,\text{if}x\ge 5,}$
Find the constants, if the function is continuous on the entire line.

x=-8, when ${\displaystyle y=-\frac{1}{4}}$ in an inverse variation.
Find y, when x=4.

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 graphs

By using the transformation of function ${\displaystyle y=x^2}$,
sketch the function of y=${\displaystyle \frac{{(x-2)}^2}{3}+4}$

g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f.${\displaystyle g\left(x\right)=\frac{1}{3}{(x-2)}^3}$

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
$h(x)=|x+3|-5.$