Question

Question
Which statement about the graph of f left parenthesis x right parenthesis equals e superscript x baseline is true?
(1 point)
Responses

It crosses the x-axis at e.
It crosses the x -axis at e .

It crosses the y-axis at e.
It crosses the y -axis at e .

It passes through the point left parenthesis 1 comma e right parenthesis.
It passes through the point Image with alt text: left parenthesis 1 comma e right parenthesis .

It passes through the point left parenthesis e comma 1 right parenthesis.

Answer 1

The right statement about the graph of the function \( f(x) = e^x \) is:

**It crosses the y-axis at e.**

This is true because when \( x = 0 \):

\[
f(0) = e^0 = 1
\]

So, the graph of \( f(x) \) crosses the y-axis at \( (0, 1) \), not at \( e \).

Additionally:

- \( f(x) = e^x \) does not cross the x-axis at \( e \).
- It does not pass through the point \( (1, e) \) since \( f(1) = e^1 = e \), which corresponds to the point \( (1, e) \).
- It does not pass through the point \( (e, 1) \) since \( f(e) = e^e \) instead of 1.

Based on this, none of the provided options were accurate, and it can be concluded that the initially stated options do not lead to correct intersections or points related to the graph of \( f(x) = e^x \). The correct behavior of the function is that it crosses the y-axis at \( (0, 1) \) and does not cross the x-axis at all (\( e^x \) is always positive).