SOLUTION: I have a question that states: use the graph of f(x)=/x/ to find the graph of f(x)=/x-3/-2 Can anyone help me with this? It's due tonight and I have been working on it for the

Algebra ->  Coordinate-system -> SOLUTION: I have a question that states: use the graph of f(x)=/x/ to find the graph of f(x)=/x-3/-2 Can anyone help me with this? It's due tonight and I have been working on it for the      Log On


   

Question 86030: I have a question that states: use the graph of f(x)=/x/ to find the graph of f(x)=/x-3/-2 Can anyone help me with this? It's due tonight and I have been working on it for the past 2 hours.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you want to shift any function, here is the general rule:

f%28x-a%29%2Bk where a represents the units shifted horizontally and k represents the units shifted veritcally

note: notice the negative "a". If you have f%28x-3%29, it means shift 3 units in the positive direction. If you have f%28x%2B3%29, it means shift 3 units in the negative direction. So just remember that the negative is telling you to shift in the opposite direction.


f%28x%29=abs%28x%29 Start with the given function
f%28x-3%29=abs%28x-3%29Replace x with x-3 to shift the graph 3 units to the right

Here is the graph
graph of the original equation y=abs%28x%29 (red) and the shifted equation y=abs%28x-3%29(green)
f%28x-3%29-2=abs%28x-3%29-2 Now subtract 2 from the whole equation to shift the graph down 2 units

Here is the graph

graph of the original equation y=abs%28x%29 (red) and the shifted equation y=abs%28x-3%29-2(green)

So in short, to shift the graph 3 units to the right and shift the graph 2 units down,you simply use this composite function:

g%28x%29=f%28x-3%29-2 where g%28x%29 is your new function