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 " .
