Explain why the initial value of any function of the form f (x) = a (bx) is equal to a.

Are you sure it's not f (x) = a (b^x) because anything to the power of 0 equals one and ax1 will always be a. if the equation is just f (x) = a (bx) then the initial value shouldn't be a because x = 0

When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a.