To determine the coordinates of the $y$-intercept of the function $g(x) = -2(2^{-x}) - 2$, we need to evaluate the function when $x = 0$. The $y$-intercept occurs where the graph crosses the $y$-axis, which corresponds to $x = 0$.

Substitute $x = 0$ into the function:

$g(0) = -2(2^{-0}) - 2$

Since $2^{-0} = 2^0 = 1$, the equation simplifies to:

$g(0) = -2(1) - 2 = -2 - 2 = -4$

Thus, the coordinates of the $y$-intercept are:

$\text{Coordinates of } y\text{-intercept: } (0; -4)$

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. How would you find the $x$-intercept of the function $g(x)$?
2. What does the $y$-intercept represent in the context of the graph of $g(x)$?
3. How would the $y$-intercept change if the function were $g(x) = -2(2^{-x}) + 3$?
4. How can you verify the $y$-intercept graphically using a plot of $g(x)$?
5. What is the effect of the negative sign in front of the exponential term on the graph of $g(x)$?

Tip: When calculating intercepts, substitute either $x = 0$ for the $y$-intercept or $y = 0$ for the $x$-intercept and solve the resulting equation.