To find the rate of change of the function \( f(x) = \frac{3}{2}x + 5 \), we need to calculate its derivative, as the derivative represents the rate of change of the function with respect to \( x \).
The function \( f(x) \) is a linear function. The derivative is calculated as follows:
\[ f'(x) = \frac{d}{dx} \left( \frac{3}{2}x + 5 \right) \]
The derivative of \( \frac{3}{2}x \) is \( \frac{3}{2} \), and the derivative of the constant \( 5 \) is \( 0 \). Thus, we have:
\[ f'(x) = \frac{3}{2} \]
This means that the rate of change of \( f(x) \) is constant and equal to \( \frac{3}{2} \). So, for every unit increase in \( x \), \( f(x) \) increases by \( \frac{3}{2} \).