To determine the correct statement about the functions \( f(x) = -2x + 5 \) and \( g(x) \), we need to analyze the properties of \( f(x) \) and how \( g(x) \) behaves based on the information in the table (which we don't have explicit values for).
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Analyzing \( f(x) \):
- The function \( f(x) = -2x + 5 \) is a linear function with a negative slope of -2.
- A negative slope means that as \( x \) increases, \( f(x) \) decreases. Therefore, \( f(x) \) is a decreasing function.
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Analyzing \( g(x) \):
- Without the actual values from the table for \( g(x) \), we can't definitively tell whether \( g(x) \) is increasing or decreasing. Normally, we would analyze the values given in the table to determine if \( g(x) \) has an upward or downward trend.
Since we only know that \( f(x) \) is decreasing, we can't accurately select an answer about \( g(x) \) without its specific behavior. However, we can state:
- If \( g(x) \) is provided to be decreasing in the table, then option A would be correct.
- If \( g(x) \) is provided to be increasing, then option B would be correct.
- If both \( g \) and \( f \) are increasing, option C would be correct.
- If both are decreasing, option D would be correct.
In conclusion, without knowledge of \( g(x) \)’s behavior, the definitive statement is that \( f(x) \) is a decreasing function. The truth of the other statements relies entirely on the specific properties of \( g(x) \) as shown in the table. Thus, if you can provide the values for \( g(x) \) or describe its behavior, I could give you a more conclusive answer.
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