Here is the graph of the function:

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

This curve represents exponential decay since the base $\frac{1}{2} < 1$. The function decreases rapidly as $x$ becomes more positive.

Would you like more details or have any questions?

Here are 8 related questions to explore:

1. How does the graph change if the coefficient 2 is increased or decreased?
2. What happens to the graph if the base $\frac{1}{2}$ is replaced by a number greater than 1?
3. How can you determine the horizontal asymptote of this function?
4. How would the graph look if you reflected it across the y-axis?
5. What is the y-intercept of this function, and how is it calculated?
6. How does changing $x$ in the exponent affect the steepness of the curve?
7. What are some real-life examples of exponential decay modeled by functions like this?
8. How does the rate of decay change if the base is smaller, like $\frac{1}{3}$ instead of $\frac{1}{2}$?

Tip: Exponential decay functions have a base between 0 and 1, causing the graph to approach the x-axis as $x$ increases.