The graph of f(x) = -3^x - 2 is a downward-sloping exponential function with alternating signs for even and odd x. It approaches but never reaches the horizontal asymptote y = -2. (option A, top left graph)
The function f(x) = -3^x - 2 represents an exponential function with a base of -3. Here's how you can understand and visualize the graph:
1. Base and Sign:
- Since the base is -3, the function will alternate signs as x changes between even and odd integers. For even values of x, the result will be positive, and for odd values, it will be negative.
2. Asymptote:
- Exponential functions often have horizontal asymptotes. In this case, as x approaches negative or positive infinity, the function will approach but never reach the horizontal line y = -2.
3. Shift:
- The constant term (-2) shifts the entire graph downward by two units.
4. Graph Behavior:
- The graph will decrease rapidly as x increases because of the negative base, and it will increase as x decreases.
Putting it all together, the graph of f(x) = -3^x - 2 will show a rapidly decreasing exponential function that alternates between positive and negative values, and it will have a horizontal asymptote at y = -2. The specific shape will depend on the values of x considered. It's recommended to use graphing software or calculators to visualize the graph accurately.
Hence, option A (the top left graph) is the correct answer.
The complete question is:
(attached)