To find the graph of the first and the second function, let's substitute x by 1 and find the function that has the corresponding y value.
a)
![\begin{gathered} f(x)=2^x \\ f(1)=2^1 \\ f(1)=2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/h0gtk98xoi503bfzym22d8o161xyctdcqc.png)
The graph that has the point (1, 2) is the green graph.
b)
![\begin{gathered} f(x)=3^x \\ f(1)=3^1 \\ f(1)=3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/t0puu0ic6sgtw2usdiugxnybmn9oxuxl5j.png)
The graph that has the point (1, 3) is the yellow graph.
To find the graph of the third and the fourth function, let's substitute x by -1 and find the function that has the corresponding y value.
c)
![\begin{gathered} f(x)=((1)/(2))^x \\ f(-1)=((1)/(2))^(-1) \\ f(-1)=((2)/(1))^1 \\ f(-1)=2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/q694fbesqh8pgg703rmvrdida215z7z7eu.png)
The graph that has the point (-1, 2) is the blue graph.
d)
![\begin{gathered} f(x)=((1)/(3))^x \\ f(-1)=((1)/(3))^(-1) \\ f(-1)=((3)/(1))^1 \\ f(-1)=3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/f6v2nvrtsn5jxtgg102axfrsxc20570ada.png)
The graph that has the point (-1, 3) is the red graph.
Answer:
![\begin{gathered} f(x)=2^x\Rightarrow g \\ f(x)=3^x\operatorname{\Rightarrow}y \\ f(x)=((1)/(2))^x\operatorname{\Rightarrow}b \\ f(x)=((1)/(3))^x\operatorname{\Rightarrow}r \end{gathered}]()