20 points and crown! this table shows input and output values for a linear function f(x) . what is the difference of outputs for any two inputs that are one value apart? −1 0.25 0.5 1 x f(x) −3 −0.5 −2 0 −1 0.5 0 1 1 1.5 2 2 3 2.5

The answer is:  [C]:  " 0.5 " .

Explanation:

Let us examine all the inputs ("x-values") listed that are "one unit apart"; and see what the corresponding "outputs" (that is:  the "f(x)" values) are—and how far apart the corresponding  "outputs" are.

Refer to the table (provided within the actual question):; 

          → And start with the beginning values for the "inputs" (or; "x-values") listed; which are in "chronological order", from:  "x = -3" to "x = 3" ; and all the "x-values" provided are "1 (one) unit apart" ;  and: "inn chronological order, from least ("x = -3") to greatest ("x = 3")" . 

  When:  x = -3 ;  f(x) = -0.5 ; 
  
  When:  x = -2 ;  f(x)  =  0 .

 The inputs, "-3" and "-2" , are ONE (1) unit apart.
  
      → Note:  | [-3 − (-2)] | = | (-3+2) |  = | (-1) | = " 1 " (one) unit apart.
 
 The corresponding "outputs" are "0.5 units apart" . 

   Note:  | (-0.5 − 0) |  = | (-0.5) | = 0.5 ;  → "0.5 units apart" . 

           Then continue, in chronological order, with the values listed on the table (provided within the actual question):

  When:  x = -2 ;  f(x) = 0 ; 
  
  When:  x = -1 ;  f(x)  = 0.5  ;

 The inputs, "-2" and "-1" , are ONE (1) unit apart.
   
      → Note:  | [-2 − (-1)] | = | (-2 + 1) |  = | (-1) | =  " 1 " (one) unit apart.

 The corresponding "outputs" are "0.5 units apart" ;  

   Note:  | (0 − 0.5 |  = | (-0.5) | = 0.5 ;  → "0.5 units apart" .

       Then continue, in chronological order, with the values listed on the table (provided within the actual question):

  When:  x = -1 ;  f(x) = 0.5 ; 
  
  When:  x =  0 ;  f(x)  = 1  ;

 The inputs, "-1" and "0" , are ONE (1) unit apart.
  
      → Note:  | (-1 − 0) |  =  | (-1) |  =  " 1 " (one) unit apart. 
 
The corresponding "outputs" are "0.5 units apart" ;  

   Note:  | (0.5 − 1 |  = | (-0.5) | = 0.5 ;  → "0.5 units apart" .

       Then continue, in chronological order, with the values listed on the table (provided within the actual question):

  When:  x = 0;  f(x) = 1 ; 
  
  When:  x = 1 ;  f(x)  = 1.5  ;

 The inputs, "0" and "1" , are ONE (1) unit apart.
  
      → Note:  | (0 − 1] | = | (-1) | = " 1 " (one) unit apart. 
 
The corresponding "outputs" are "0.5 units apart" ;  

   Note:  | ( 1 − 1.5) |  = | (-0.5) | = 0.5 ;  → "0.5 units apart" .

        Then continue, in chronological order, with the values listed on the table (provided within the actual question):

  When:  x = 1 ;  f(x) = 1.5 ; 
  
  When:  x = 2 ;  f(x) = 2  ;

 The inputs, "1" and "2" , are ONE (1) unit apart.
  
      → Note:  | (1 − 2)] | = | (-1) | = " 1 " (one) unit apart. 
 
The corresponding "outputs" are "0.5 units apart" .

   Note:  | (1.5 − 2 |  = | (-0.5) | = 0.5 ;  → "0.5 units apart" .

      Then continue, in chronological order, with the values listed on the table (provided within the actual question):

  When:  x = 2 ;  f(x) = 2 ; 
  
  When:  x = 3 ;  f(x)  = 2.5  ;

 The inputs, "2" and "3" , are ONE (1) unit apart.
 
    Note:   | (2 − 3) |  = | (-1) | =  " 1 " (one) unit apart.

 The corresponding "outputs" are "0.5 units apart" ;  

   Note:  | (2 − 2.5 |  = | (-0.5) | = 0.5 ;  → "0.5 units apart" .

 So; as calculated:  The answer is that the outputs are:

    " 0.5 " [units apart]  ;   which is:  Answer choice:  [C]:  " 0.5 " .

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