Final answer:
The correct statement about the graph of f(x) = e^x is that it passes through the point (1, e), which corresponds to the function value at x = 1. The other options are incorrect as the graph of an exponential function never crosses the x-axis and f(x) = e^x crosses the y-axis at (0, 1), not at (0, e). So, the correct answer is C. It passes through the point (1, e).
Step-by-step explanation:
The question is asking which statement about the graph of the exponential function f(x) = e^x is true. To determine the correct answer, we examine the behavior of the function at certain points.
Option A suggests the function crosses the x-axis at x = e, which would mean f(e) = 0. However, for any value of x, e^x is never zero.
Option B suggests the function crosses the y-axis at y = e, but the graph of f(x) = e^x crosses the y-axis at (0,1) because e^0 = 1.
Option C is that the graph passes through the point (1, e). This is true since f(1) = e^1 = e.
Option D suggests the graph passes through the point (e, 1), which is not correct since f(e) = e^e, not 1.
Therefore, the correct answer is C. It passes through the point (1, e).