To determine which function has the greater rate of change, we need to analyze the given functions.
Function 1: \( f(x) = 32x + 5 \)
- The rate of change for a linear function is given by the coefficient of \( x \), which in this case is \( 32 \).
Function 2: It is described as a diagonal line connecting two data points, but we don't have specific information about its slope. For a diagonal line, the rate of change (slope) would be equal to the change in \( y \) divided by the change in \( x \) between the two points. Without specific values, we cannot determine the exact rate of change.
Therefore, if the diagonal line's slope is less than \( 32 \), then Function 1 has the greater rate of change.
Since there is no information provided for Function 2 to ascertain its slope, we cannot definitively say which function has a greater rate of change without additional information.
However, typically in problems like these, if no specific numbers suggest the slope of Function 2 is greater than Function 1, we might assume that:
Function 1 has a greater rate of change. Therefore, the answer is:
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