Question

What function is represented below? graph begins in the first quadrant and decreases quickly while crossing the ordered pair 2, 1. Then the graph 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) = one fourth to the power of x-2 f(x) = (1/4)^(x-2)
It is a decreasing function that when x= 2, (1/4) is raised to the zero power which is 1, which is what the point (2,1) asks for.

Answer 2

The represented function is :

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

Explanation:

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

And the equation must pass through (2,1) as given,

But, f(2) = 2.0625 ≠ 1 so this is not the required function.

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

And the equation must pass through (2,1) as given,

But, f(2) = 0.0039 ≠ 1 so this is not the required function.

`3.\thinspace f(x)=((1)/(4))^x -2`

And the equation must pass through (2,1) as given,

But, f(2) = -1.94 ≠ 1 so this is not the required function.

`4.\thinspace f(x)=((1)/(4))^(x-2)`

And the equation must pass through (2,1) as given,

We see, f(2) = 1 so this is the required function and the corresponding graph of the function is attached below :

Hence, The correct option is (4)