To determine which function has the greater rate of change, we need to analyze the rate of change of each function.
For Function 1: \( f(x) = \frac{3}{2}x + 5 \)
The rate of change (or slope) of a linear function in the form \( y = mx + b \) is given by the coefficient of \( x \). Here, the slope \( m = \frac{3}{2} \).
For Function 2: A diagonal line connects two data points on a coordinate plane. The slope of this line can vary depending on the specific data points chosen. However, without specific coordinates for the two points, we cannot determine its slope.
Assuming that Function 2 is constructed from points that value a slope of \( \frac{3}{2} \) or lower, we can conclude that:
- If Function 2 has a slope greater than \( \frac{3}{2} \), it has a greater rate of change.
- If Function 2 has a slope equal to or less than \( \frac{3}{2} \), then Function 1 has a greater rate of change.
Since we do not know the specific slope of Function 2, we cannot definitively say which has a greater rate of change.
However, based solely on the information given, with no specific data points provided for Function 2, the safest assumption is that without further information, the rate of change of Function 1 is \( \frac{3}{2} \).
Thus the answer is based on the known rate of change:
Type 1 for Function 1.