When graphing a radical, such as the square root function y = √
x , remember that the domain (the valid values for x) is all non-negatve numbers,
and the range (all valid values of y) is also all non-negative numbers. When you adjust the equation by adding something after the root, such as
y = √
x + k, the domain stays the same but the range changes to all numbers greater than or equal to k, since you in essence shift the original
graph up k units. Likewise when you adjust by subtracting something inside the root, such as y = √
x - h , the range stays the same, but
the domain changes to all real numbers greater than or equal to h since you shift the graph left h units. Combining these gives us the general form:
y = √
x - h + k
Will have a domain x ≥ h and a range y ≥ k.