In this student problem I made my own example of a graphing exponential equation. The first step in these types of problems is finding your a, h, b, and k. 'a' tells you if the graph is above or below the asymptote by the sign. If it is postive then it is above and if it is negative then it is below. B tells you what side, right or left, the graph is. If the absolute value of b is less then one (fraction) then it goes on the right side. If the absolute value of b is greater than 1 then it is on the left side of the asymptote. You find h by setting the exponent equal to zero and this shifts the graph left and right but for this example the key points do the shift. 'k' tells you if the asymptote moves up or down. If it is positive then it moves up units but if it is negative it moves down. You find the key points by adding four numbers to the 3rd key point. You find the asymptote by just looking at k because y=k. You find the x-intercepts by plugging in zero for y and for the y-intercepts you plug in 0 for x. The domain for these probelms will always be (-inf, inf) because an exponential graph has an asymptote of y=k, leading to no restrictions to the domain. The range depends on the asymptote. Lastly for the graph, you just plot in the key points and the intercepts.
The trickets part of these types of problems is probably finding the x-intercept. It was the trickets part for me because you need to make sure you divide by ln correctly and do all your intermediate steps correctly as well. Another tricky part of this problem will have to be the graphing. You need to make sure you do not cross the asymptote, plot each point you find correctly, and go in the right direction.
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