The given function is:

$f(x) = -2(3)^x - 5$

This is an exponential function, where the general form is:

$f(x) = a(b)^x + c$

Here:

• $a = -2$ (the coefficient determines the vertical stretch or compression and the direction of the graph),
• $b = 3$ (the base of the exponential function),
• $c = -5$ (the vertical shift).

Would you like me to:

1. Graph the function,
2. Find its domain and range,
3. Analyze its behavior (asymptotes, intercepts, etc.),
4. Solve for specific values of $f(x)$,
5. Discuss transformations compared to the base function $f(x) = 3^x$?

Let me know, or if you have another request!

Here are five related questions:

1. What is the y-intercept of the function $f(x)$?
2. How does the graph behave as $x \to \infty$ and $x \to -\infty$?
3. How would the function change if $a = +2$ instead of $-2$?
4. Can you solve for $x$ if $f(x) = 0$?
5. How does the base $b = 3$ affect the growth rate compared to $b = 2$ or $b = 4$?

Tip: Always note the sign of $a$ in exponential functions—it determines whether the graph increases or decreases as $x$ grows.