The function g(x) is graphed.

On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- and y-axis at (0, 0), and leaves the plane at point (2.3, 5).

Which statements about the function are true? Choose three options.

g of 1 = negative 1
g of 0 = 0
g of 4 = negative 2
g of 1 = 1
g of negative 1 = 1

1 answer

Based on the description of the graph of the function \( g(x) \):

1. The function \( g(x) \) crosses the origin at (0, 0), so \( g(0) = 0 \).
2. The function is symmetric around the y-axis, as indicated by the points (negative 2.3, 5) and (2.3, 5), and the crossing points.

Let's analyze each of the given statements:

1. \( g(1) = -1 \) - Based on the description, we do not have enough information to determine the exact value at \( x = 1 \).
2. \( g(0) = 0 \) - This is true since the function crosses the y-axis at the origin.
3. \( g(4) = -2 \) - The description does not provide any information about the function at \( x = 4 \).
4. \( g(1) = 1 \) - Based on symmetry and not enough data given, this cannot be confirmed or denied with certainty.
5. \( g(-1) = 1 \) - This seems consistent with the symmetry and general shape suggested, but without precise data at \( x = -1 \), it cannot be absolutely confirmed.

From the information given, the following statements are most likely correct:

1. \( g(0) = 0 \) (as this is directly referenced by the graph)
2. \( g(-1) = 1 \) could be consistent with symmetry, but strictly speaking from the precise data
3. \( g(2.3) = 5 \) and \( g(-2.3) = 5 \) are implicitly true - specifically looking at the crossing points outside standard options given.

Given the choices strictly:

- \( g(0) = 0 \)
There appear conflicts as precise `I'm backing only choice confidently`

Thus for completeness follow, the remaining selection conflict directly provided data `Hence likely best suited option directly and summarized in graph views`()
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