# Drawing Graph of the Function y=f(x-a)+b

To draw graph of the function y=f(x)+b we need to shift graph of the function b units up if b>0, or b units down if b<0 (see figure to the right).

To draw graph of the function y=f(x-a) we need to shift graph of the function a units right if a>0, or a units left if a<0 (see figure to the left).

So, to draw graph of the function y=f(x-a)+b we need to perform 3 steps:

1. Draw graph of the function y=f(x);
2. Shift it b units up if b>0 and b units down if b<0;
3. Shift result of second step a units right if a>0 and a units left if a<0;

Note, that we can first perform step 3 and then step 2.

Example . Draw graph of the function y=sqrt(x-2)+4.

Here a=2 and b=4, so we draw graph of the function y=sqrt(x) and then shift it 2 units to the right and 4 units up (see figure to the right).