In this Section:
In this section, we learn how to find the vertical or horizontal transformation of an elementary function. We will look at the graphs of the absolute value function, the square root function, the reciprocal function, and the greatest integer function (sometimes called the floor function). To find the horizontal shift, we examine what’s happening inside of our function. We can say f(x-h), represents a shift to the right by h units, if h is a positive number. We can also say f(x+h) represents a shift to the left by h units, if h is a positive number. To find the vertical shift, we think about what is happening outside of our function. When we have a vertical shift up by k units, we see f(x) + k, where k is a positive number. When we see a vertical shift down by k units, we see f(x) - k, where k is a positive number. In many cases, our function will have both a vertical and horizontal shift.