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Which statement about the graph of f(x)=e^x is true?

A. It crosses the x-axis at e.
B. It crosses the y-axis at e.
C. It passes through the point (1,e).
D. It passes through the point (e,1).

1 Answer

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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).

User Nick Dixon
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