[d] Creating the logarithmic function graph using the inverse function properties
Step1: Reflect the five points (A, B, C, D, and E) you obtained from the table of values, as well as the exponential function curve, across the line $y=x$.
Use the following commands
points = {A,B,C,D,E}
Reflect(points, y=x)
g = Reflect(f, y=x)
[e] Step2: Next, graph the logarithmic function by typing $h(x) = log_8(x)$ and the axis of reflection by typing $y=x$.
Verify that the graph of the logarithmic function $h(x)$ coincides with the reflected curve $g(x)$ from Step 1.
Submit a screenshot from GeoGebra, making sure that all five reflected points, the reflected curve $g(x)$ from Step 1, and the logarithmic function $h(x)$ curve are clearly visible, along with the axis of reflection.
[f] Interpretation: Reflect on your discovery that the exponential function curve $f(x) = 8^x$ and the corresponding logarithmic curve are inverse functions: Was this outcome unexpected?
Rather than simply stating "this is not unexpected" or "this is unexpected," provide a detailed explanation of your findings.
Discuss the mathematical principles that explain why the exponential and logarithmic curves are inverses of each other, and why the curves behave as they do.
Hint: Start by determining the coordinates of the five reflected points based on your graphical work.