A function in the form is an exponential function. If
a > 0, and b > 1 -- this is exponential growth function
a > 0, and 0 < b < 1 -- this is exponential decay function
The given function can be written as , so a > 0 and 0 < b < 1, hence this is exponential decay function.
For end behavior, we take limits from -∞ and from ∞. If we do that we can see that C is the correct answer. Also, looking at the graph explains it. Attached is the graph.
<em>From the graph, as we move towards negative infinity, the graph goes towards positive infinity and as we move towards positive infinity, the graph goes towards 0.</em>
Take point (3, 2) and first translate it left one unit. Now the point is (2, 2)
Now reflect it over the y-axis. Doing so keeps the y value the same, we have a vertical line of reflection, so we are only changing the distance to the y-axis, which is the x-value.
Our x value is 2 units away from the y axis, so its reflection will be 2 units away on the other side of the axis.