The function \( f(x) = 2^x \) is an exponential function that grows rapidly as \( x \) increases. The graph of \( f(x) \) is above the x-axis for all values of \( x \), starting from \( (0, 1) \), and approaches the x-axis (but never touches it) as \( x \) approaches negative infinity.
The function \( -f(x) = -2^x \) reflects the original graph of \( f(x) \) across the x-axis. This means that every point \( (x, 2^x) \) on the graph of \( f(x) \) will have a corresponding point \( (x, -2^x) \) on the graph of \( -f(x) \).
Key characteristics of the graph of \( -f(x) \):
- It will approach the x-axis (but never touch it) as \( x \) approaches positive infinity.
- It will dive deeper into the negative y-values as \( x \) approaches negative infinity.
- The graph will have its y-intercept at \( (0, -1) \).
If you have a set of options (like multiple-choice answers), look for the graph that shows an exponential curve below the x-axis, starting at \( (0, -1) \) and trending downward as \( x \) moves towards the left, while approaching the x-axis as \( x \) moves to the right.