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` unitsshifting graph of the function up and down 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;

shifting graph of the function left and right

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 upshifting the function up and right (see figure to the right).