[tex]\begin{gathered} f(x)=ab^x \\ \text{for (}0,1\text{)} \\ 1=ab^0 \\ 1=a(1) \\ a=1 \\ \text{for (}1,\frac{1}{3}\text{)} \\ \frac{1}{3}=(1)b^1 \\ \\ \frac{1}{3}=b \\ The\text{ base is }\frac{1}{3} \\ f(x)=1\cdot(\frac{1}{3})^x \\ f(x)=(\frac{1}{3})^x \\ The\text{ domain is all real numbers or (-}\infty,\infty\text{)} \end{gathered}[/tex]
