Question

Which of the following is the function representing the graph below?

F(x)=4^x

F(x)=4^x-3

F(x)=4^x+3

F(x)=4^(x+3)

Answer 1

F(x)=4^(x+3) representing the graph

Answer 2

Hence, the function representing in the graph is:

`F(x)=4^(x+3)`

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)

`F(x)=4^x`

when x= -3 we have:

`F(3)=4^(-3)=(1)/(4^3)=(1)/(64)\\eq 1`

Hence, option: 1 is incorrect.

B)

`F(x)=4^x-3`

when x= -3 , we get:

`F(-3)=4^(-3)-3\\\\F(-3)=(1)/(64)-3\\eq 1`

Hence, option: B is incorrect.

C)

`F(x)=4^x+3`

when x= -3 , we get:

`F(-3)=4^(-3)+3\\\\F(-3)=(1)/(64)+3\\eq 1`

Hence, option: C is incorrect.

D)

`F(x)=4^(x+3)`

when x= -3 , we get:

`F(-3)=4^{{-3}+3}\\\\F(-3)=4^0=1`

Hence, option: D is correct.