The correct equation of the graph shown is:

D) $f(x) = \left(\frac{1}{2}\right)^x$

Would you like any further details or explanations?

Here are 5 related questions to deepen your understanding:

1. What properties define exponential decay functions like $f(x) = \left(\frac{1}{2}\right)^x$?
2. How does changing the base of an exponential function affect its graph?
3. How can you determine the base of an exponential function from its graph?
4. What happens to the graph of $f(x) = \left(\frac{1}{2}\right)^x$ if the base changes to a value greater than 1?
5. How does the graph of $f(x) = -\left(\frac{1}{2}\right)^x$ differ from $f(x) = \left(\frac{1}{2}\right)^x$?

Tip: Exponential decay functions have bases between 0 and 1, leading the graph to decrease as $x$ increases.