Question 107446

<pre>
       ___
f(x)= <font face = "symbol">Ö</font>x-4

The 4 shifting rules are:

1. If +C is added to the right side of f(x), the graph is shifted
   +C units UPWARD
2. If -C is added to the right side of f(x), the graph is shifted
   +C units DOWNWARD
3. If x+C is substituted for x in the right side of f(x), the graph
   is shifted C units TO THE LEFT
4. If x-C is substituted for x in the right side of f(x), the graph
   is shifted C units TO THE RIGHT

We observe that the right side of the equation 
        ___
f(x) = <font face = "symbol">Ö</font>x-4

is just like the right side of the equation 
     _
y = <font face = "symbol">Ö</font>x

which has as its graph the green curve below:

{{{ drawing(400,230,-2,10,-2,5,
    graph(400,230,-2,10,-2,5,0,sqrt(x)*sqrt(6-x)/sqrt(6-x)) )}}} 

except that x-4 is substituted for x in the right side of f(x),
so rule 4 applies and the graph is shifted 4 units TO THE RIGHT
like the green curve on the right below:

{{{ drawing(400,230,-2,10,-2,5,
    graph(400,230,-2,10,-2,5,0,sqrt(x)*sqrt(6-x)/sqrt(6-x) ),
    graph(400,230,-2,10,-2,5,0,sqrt(x-4)) )}}}

Then we erase the green curve on the left that was shifted, and
the final graph is:

{{{ drawing(400,230,-2,10,-2,5,
    graph(400,230,-2,10,-2,5,0),
    graph(400,230,-2,10,-2,5,0,sqrt(x-4)) )}}} 

Edwin</pre>