Transformations

In order to graph the function y = 2^x + 4, the graph of y = 2^x is translated up 4 units on the coordinate plane. This will shift the asymptote of the graph from y = 0 to y = 4. Note on the table below, the y-intercept has shifted up 4 units from 1 to 5 and the decimal values are getting closer and closer to the number 4.

Therefore, adding a constant (k) will move the graph, and the horizontal asymptote up k units. Subtracting a constant (k) will move the graph, and the horizontal asymptote down k units.