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I noticed that the graphs of y=4^x and y=4^-x were the same, but were on different sides of the y-axis. They also had the same y-intercept. In our graph(y=4^x), the graph always approaches the x-axis, however it never touches it. This line which the graph approaches is called the asymptote. In this case, the asymptote is the x-axis. Adding a constant to the function would also move the graph along the y-axis (vertically) and adding a constant to the exponent would move the graph along the x-axis (left and right). Finally, adding a negative sign in front on the base would reflect the graph along the x-axis.