An exponential function is typically of the form \( y = a \cdot b^x \), where \( a \) is a constant, \( b \) is a positive constant, and \( x \) is the variable.
From the options provided:
- \( y = 3x \) - This is a linear function.
- \( y = 2x - 4 \) - This is also a linear function.
- \( y = x^3 \) - This is a polynomial function.
- \( y = 3 + 5^z \) - This is an exponential function because it involves a constant added to an exponential term \( 5^z \).
Thus, the exponential function from the options given is \( y = 3 + 5^z \).