To shift the graph of $f(x) = -2^x$ left by 1 unit, we modify the input variable $x$ by adding 1 inside the function. A leftward shift of the graph is achieved by replacing $x$ with $x+1$ in the function's equation.

Thus, the equation of the function $g(x)$ that represents the graph of $f(x)$ shifted left by 1 unit is:

$g(x) = -2^{x+1}$

This transformation shifts the graph of $f(x) = -2^x$ left by 1 unit.

Do you have any questions or want more details on this? Here are some related questions for further understanding:

1. How would shifting the graph right by 2 units affect the equation of $f(x)$?
2. What happens to the graph if we shift it up or down?
3. How can we reflect the graph of $f(x)$ across the x-axis?
4. What is the effect of changing the base from 2 to another number?
5. How does the graph of $g(x) = -2^{x+1}$ differ visually from $f(x) = -2^x$?

Tip: Shifting a graph left or right always involves changing the variable inside the function's input, while up/down shifts modify the output directly.