F(x)=128(0.5)^x

(0, 1)

(1, 64)

(3, 16)

(8, 0.5)

The correct answers are:

Answer choices:

[B]: (1, 64)
[C]: (3, 16)
[D]: (8, 0.5)

Explanation:

For clarity, let us rewrite the problem as:

F(x)=128* (0.5)ˣ   

Examine our answer choices;

  [all of which are given as ordered pairs:  "(x, y)".].

Start with the first "Answer Choice: [A]": (0, 1).
    Is this correct?
   (In other words, when "x" = 0; does "y" = 1 ?

Looking at the problem:

F(x)=128* (0.5)ˣ ;   If  x = 0, then y = 128.  

(0.5)⁰ = 1 ;  Then 128 * 1 = 128.  

So, answer choice: [A]:  (0, 1): is incorrect).
 
Now let us examine answer choice: [B]:  (1, 64)

Given our problem: 

F(x)=128* (0.5)ˣ ;  When we substitute "1" for "x", do we get "64"?

128 * (0.5)¹ =? 64? ;  Note:  (0.5)¹ = 0.5; so: 

128 * (0.5)¹ = 128 * (0.5) = 64 . Yes! 
So this answer choice, "Answer choice: [B]: (1, 64)", is correct.

Technically, there could be multiple correct answer choices, so let us examine the rest of the answer choices given:

Let us examine answer choice: [C]: (3, 16) .

Given: F(x)=128* (0.5)ˣ ; when we substitute "3" for "x", do we get "16"?

Let us substitute "3" for "x"; and write as: 

F(x)=128 * (0.5)³  ;  Note: (0.5)³ = 0.125 = 1/8 ; so:

128 * (0.5)³ = 128 * 0.125 = 128 * (1/8) = 16.  Yes.

So this answer choice, "Answer choice: [C]: (3, 16)" is correct.

Let us examine answer choice: [D]: (8, 0.5) .

Given: F(x)=128* (0.5)ˣ ; when we substitute "8" for "x", do we get "0.5"?

Let us substitute "8" for "x"; and write as: 

F(x)=128 * (0.5)⁸   ;  Note: (0.5)⁸  = 0.00390625 = 1/256 ; so:

128 * (0.5)⁸  = 128 * 0.00390625 = 128 * (1/256) = 0.5.  Yes.

So this answer, "Answer choice: [D]: (8, 0.5)" is correct.

Opposite angles in a cyclic quadrilateral add up to 180°