Question 1101015
<pre>
You are studying about the question:
 
"When you alter the equation, how does that alter the graph?"

Here is the graph of {{{f(x)=x^3}}} in red:

{{{graph(300,400,-2,3,-4,4,x^3)}}}

Next we take the right side of f(x), which is x<sup>3</sup> and
replace x by x-1 and call it g(x).  That graph has the exact same
shape as the graph of f(x) except that it is shifted 1 unit to the
right of f(x).  Its graph is in green below, the graph of

{{{g(x)=(x-1)^3}}}

{{{graph(300,400,-2,3,-4,4,x^3,(x-1)^3)}}}

Finally we take the right side of g(x), which is (x-1)<sup>3</sup> and
add +2 and call it h(x).  That graph has the exact same shape as the 
graph of g(x), except that it is shifted (raised) 2 unit upward.  Its 
graph is in blue below, the graph of

{{{h(x) = (x-1)^3+2}}} 

{{{graph(300,400,-2,3,-4,4,x^3,(x-1)^3,(x-1)^3+2)}}}

All three graphs have the same shape.

Edwin</pre>