To determine the true statement about the function \( f(x) = -x^2 + 8 \), let's first analyze this function.
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Identifying the maximum value of \( f(x) = -x^2 + 8 \):
- This is a quadratic function that opens downward (as indicated by the negative coefficient of \( x^2 \)).
- The maximum value of this function occurs at the vertex. The vertex can be found at \( x = -\frac{b}{2a} \), where \( a = -1 \) and \( b = 0 \) in this case.
- Thus, \( x = -\frac{0}{2(-1)} = 0 \).
- Substituting \( x = 0 \) into the function: \[ f(0) = -0^2 + 8 = 8. \]
- Therefore, the maximum value of \( f(x) = -x^2 + 8 \) is 8.
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Analyzing the graph's function:
- Without knowing the specifics of the graph's function, we cannot provide an exact analysis.
- However, to evaluate which of the given statements (A, B, C, or D) is true, we need some assumptions about the behavior (whether it has a maximum or minimum and what those values might be).
Now let's evaluate the choices:
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A) The maximum value for both functions is the same: Without specific information about the maximum value of the graph's function, we cannot confirm this statement.
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B) \( f(x) = -x^2 + 8 \) has a maximum value greater than the graph's function: This statement can't be verified without knowing the graph function’s maximum value.
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C) \( f(x) = -x^2 + 8 \) has a maximum value less than the graph's function: Similarly, we can't verify this without additional information.
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D) Both functions have a minimum value of 0: Since \( f(x) = -x^2 + 8 \) has a maximum (not a minimum) and does not reach a minimum of 0, this statement is false.
So, the correct response depends heavily on the behavior of the graph's function, which isn't provided. Based solely on the information about \( f(x) = -x^2 + 8 \), we can eliminate statements D, and we wouldn't have enough information to confirm A, B, or C without additional details about the graph's function. Therefore, with the information given, none of the statements can be determined to be true.