Answer:
Hence, the function representing in the graph is:
[tex]F(x)=4^{x+3}[/tex]
Step-by-step explanation:
Clearly after looking at the given graph of a function we could observe that:
when x= -3 the function takes the value as F(-3)=1
Hence, we will check in each of the options:
A)
[tex]F(x)=4^x[/tex]
when x= -3 we have:
[tex]F(3)=4^{-3}=\dfrac{1}{4^3}=\dfrac{1}{64}\neq 1[/tex]
Hence, option: 1 is incorrect.
B)
[tex]F(x)=4^x-3[/tex]
when x= -3 , we get:
[tex]F(-3)=4^{-3}-3\\\\F(-3)=\dfrac{1}{64}-3\neq 1[/tex]
Hence, option: B is incorrect.
C)
[tex]F(x)=4^x+3[/tex]
when x= -3 , we get:
[tex]F(-3)=4^{-3}+3\\\\F(-3)=\dfrac{1}{64}+3\neq 1[/tex]
Hence, option: C is incorrect.
D)
[tex]F(x)=4^{x+3}[/tex]
when x= -3 , we get:
[tex]F(-3)=4^{{-3}+3}\\\\F(-3)=4^0=1[/tex]
Hence, option: D is correct.
