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.
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.
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.
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.
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.
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.
Robert Boyle was one of the most prolific figures in the scientific revolution and the leading scientist of his day. He discovered the Boyle's law, which shows that the volume and pressure of a gas are proportionally related.
