Final answer:
The correct answer is option B. Based on the graph of function g(x) that crosses the origin, the correct answer is B. g of 0 = 0, as it confirms the function's value at the origin. Other options provided cannot be verified without additional information about the function.
Step-by-step explanation:
The student inquires about the properties of function g(x) based on its graph. Given that it passes through the origin (0,0) and the description of the graph, which enters and leaves the plane at symmetric points with regard to the x-axis, we can infer that g(x) is an odd function. This means for every x, g(-x) = -g(x). Based on this, we can analyze the options given:
- A. g of 1 = negative 1: With the provided information, we cannot confirm this without more information about the actual function.
- B. g of 0 = 0: This is true because the graph crosses the origin; hence g(0) is indeed 0.
- C. g of 4 = -2: With the provided information, we cannot confirm this without more information about the actual function or its graph beyond the described area.
- D. g of 1 = 1: With the provided information, we cannot confirm this without more information about the actual function.
- E. g of negative 1 = 1: This can be true if g(x) is an odd function because typically for an odd function, g(-x) = -g(x); if g(1) were -1, then this statement would be true. However, without more information on g(1), it is speculative.
With the given information, the option B. g of 0 = 0 is the correct answer, as it aligns with the function crossing the origin according to its graph.