SP#3: Unit I Concept 1: Finding parts and graphing exponential equations.

Steps!
1) Find your a, b, h, and k (remember that your a is first, then b, then h is either added to or subtracted from x, and k is the constant that is added or subtracted to the equation).
2) Write your asymptote. Remember the asymptote is y=k (a horizontal asymptote).
3) Then you find your x-intercept by plugging 0 in for y and solving like a regular equation for x (reminder: you will not always have an x-intercept).
4) Find your y-intercept by plugging 0 in for x and solve the equation.
6) Write your domain.
7) Write your range down ( depends on location of graph).
8) Use h as your third key point and choose two below that and one above it then use your table application to find the other point.
9) Graph it by first putting your asymptote as a dotted line, then your intercepts, and finally your key points. Then connect them appropriately and do not forget your arrows.

 

   This problem is all the steps on how to solve for exponential equations. It is an example of one without an x-intercept and it shows each step for ease. It is a walk through on how to get these types of problems done. It is all about the exponential equations and involving other ideas from other concepts. Enjoy.

 

     There are a few things that you need to pay close attention to. One is remember that the h is the opposite of what is seen in the equation. Also with exponential equations your domain will always be negative infinity to infinity. The range is different though. Remember if it is below the graph then it will be negative infinity to the asymptote and if it is above the graph then it will be the asymptote to infinity. It is easy to mess up on the little intermediate steps of solving for the intercepts so be careful and take your time. Also it is very easy to misinterpret things and end up with the wrong answer so take your time and check using the table and graph feature on your calculator. Remember there is no x-intercept because the asymptote is -2 and since the graph is below the asymptote (a is negative) then it will never cross the x-axis. Also mathematically if you wanted to verify the answer is an unreal answer meaning there is no x-intercept. Enjoy!