Question

Which function is shown in the graph below?

Answer 1

Answer:b

Step-by-step explanation: you graph each answer choice and see which one looks like the graph

Answer 2

Answer: The correct option is

(B)
`y=\left((1)/(2)\right)^(x-3)+1.`

Step-by-step explanation: We are given to select the function that is shown in the graph.

From the graph, we know that

if the function is represented by y = f(x), then f(0) = 9. That is, the value of y at x = 0 is 9.

Option (A) : Here, the given function is

`y=\left((1)/(2)\right)^(x+3)-1.`

So, at x = 0, the value of y is given by

`y(x=0)=\left((1)/(2)\right)^(0+3)-1=(1)/(8)-1=-(7)/(8)\\eq 9.`

So, this option is not correct.

Option (B) : Here, the given function is

`y=\left((1)/(2)\right)^(x-3)+1.`

So, at x = 0, the value of y is given by

`y(x=0)=\left((1)/(2)\right)^(0-3)+1=\left((1)/(8)\right)^(-1)+1=8+1=9.`

So, this option is CORRECT.

Option (C) : Here, the given function is

`y=\left((1)/(2)\right)^(x-1)+3.`

So, at x = 0, the value of y is given by

`y(x=0)=\left((1)/(2)\right)^(0-1)+3=2+3=5\\eq 9.`

So, this option is not correct.

Option (D) : Here, the given function is

`y=\left((1)/(2)\right)^(x+1)-3.`

So, at x = 0, the value of y is given by

`y(x=0)=\left((1)/(2)\right)^(0+1)-3=(1)/(2)-3=-(5)/(2)\\eq 9.`

So, this option is not correct.

Thus, (B) is the correct option.