The given function is \( f(x) = 5x + 5 \).
To determine whether the function is increasing, decreasing, constant, or not a function, we can analyze its characteristics:
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Increasing Function: A function is increasing if its derivative is positive for all \( x \). The derivative of \( f(x) \) is \( f'(x) = 5 \), which is positive for all \( x \). Therefore, the function is increasing.
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Decreasing Function: Since the derivative is positive, the function is not decreasing.
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Constant Function: A constant function has a derivative of zero. Since \( f'(x) = 5 \), it is not a constant function.
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Not a Function: The expression \( f(x) = 5x + 5 \) clearly defines a function of \( x \).
Based on this analysis, the true statement is:
a. The function is an increasing function.