Question

What function is represented below?

graph begins in the second quadrant and decreases quickly while crossing the ordered pair negative 2, 1. When the graph enters the first quadrant, it begins to decrease slowly as it approaches the x axis.

f(x) = one fourth to the power of x plus 2
f(x) = one fourth to the power of x + 2
f(x) = one fourth to the power of x minus 2
f(x) = one fourth to the power of x − 2

Answer 1

f(x) = 1/4 to the power of x + 2= 627
f(x) = 1/4 to the power of x + 2= same thing as the one above
f(x) = 1/4 to the power of x - 2= 623
f(x) = 1/4 to the power of x − 2= same thing as the one above

Answer 2

The possible function is
`f(x)=((1)/(4))^(x+2)`

A is correct.

Explanation:

The graph begins in the II quadrant and decreases quickly while crossing the ordered pair (-2,1).

When the graph enters the I quadrant, it begins to decrease slowly as it approaches the x-axis.

It is exponential decay function.

`f(x)=ab^x`

If 0<b<1 then decay.

According to option, possible function:

`f(x)=((1)/(4))^(x+2)`

1/4 <1 , Decay function

We are given a passing point (-2,1)

If we put (-2,1) into f(x). It will satisfy.

Hence, The possible function is
`f(x)=((1)/(4))^(x+2)`