SP #3: Unit I Concept 1: Graphing exponential functions and identifying x- intercept, y- intercept, asymptotes, domain, range (4 points on graph minimum)

Hey this is Michael C. from Period 5. In this picture we will be graphing an exponential equation and identifying key parts. The equation we will be using is y = 5(1/2)^(x - 1) + 1. First you will identify the a, the b, the h, and the k. The next logical thing to do is find the equation for the asymptote which should be y = k. Then You find the x- intercept by setting y to zero (it should be undefined for this problem since the asymptote is y = 1 and the graph must be above it so the graph will never come into contact with the x- axis.) and the y- intercept by setting x to zero. Domain for these problems will always be all real numbers since the graph goes infinitely to the left and right. Range will depend on the asymptote and wheter the graph is above or below it, and it's above in this problem. Next you want to use some key points and the h should be your 3rd point. Plug the equation into the calculator and use the table to get the points and plot the points. You know that the graph should be heading toward the asymptote on the right side since the absolute value of b is less than 1. And that is all.

When solving this problem one must pay attention to a few things. Firstly you must be precise in identifying a- k. Second, you must make note that the x- intercept is undefined because of the asymptote. Also, you must remember that there are no restrictions for the domain and the range depends on the asymptote.