Expert: Scott A Wilson - 1/19/2010

Question
Hi there! I have a math test tomorrow, and I am not doing so well with exponential equations. I am in algebra 2 and I'm really struggling with graphing equations. For example y=2^(x-1) -2  where do I even start here? Could you explain to me the basics when it comes to graphing these equations?

Answer
Put in various values for x.

Take x  -2, -1, 0, 1, and 2 and that will give us an idea of what the curve looks like.

At x=-2, we have y = 2^(-3) - 2, and 2^(-3) is 1/2^3,
which is 1/8, so we have 1/8 - 2 = -15/8 = -1.875.

At x=-1, we have y = 2^-2 - 2; 2^(-2) = 1/4, 1/4 - 2 = -7/4 = -1.75.

At x=0, y = 1/2 - 2 = -3/2 = -1.5.

At x-1, y = 2^0 - 2 = 1 - 2 = -1.

At x  2, y = 2^1 - 2 = 2 - 2 = 0.

Note as x increases, 2^(x-1) gets large quite fast, making the -2 mean almost nothing
and y going off to infinity.

As can be seen by graphing, the graph at a very large negative number is close to -2,
so it can be said the there is an horizontal assymptote at -2.  As x goes off to infinity,
y goes off to infinity.  The graph as an upward curve to it.  At x=0, y=-1.5.