The output for the considered rules are: Rule 1: -13, Rule 2: 36, Rule 3: -2, Rule 4: -2, Rule 5: π, Rule 6: 216 cubic cm.
What is a function?
Function is a type of relation, or rule, that maps one input to specific single output.
We're given that:
Applying all the rules, one by one:
Rule 1: Subtract -7
[tex]\rm \text{inp}ut -7 = -6 -7 = -13[/tex]
[tex]\rm (\text{inp}ut )^2 = (-6)^2 = -6\times -6 = 36[/tex]
[tex]\rm \dfrac{\text{inp}ut }{3} = \dfrac{-6}{3} = -2[/tex]
- Rule 4: Divide the input in 3
Dividing something in x parts means that thing divided by x
[tex]\rm \dfrac{\text{inp}ut }{3} = \dfrac{-6}{3} = -2[/tex]
[tex]\pi[/tex] (no use of input).These type of functions which always give same constant result, no matter what the input is, are called constant functions.
- Rule 6: Volume of cube with side length as input in cm.
Volume of a cube is the cube of its side length (raising it with power 3).
We're specified that:
Side length of the considered cube = input = -6 cm
Since length is a non-negative quantity, so we take absolute value of -6, therefore, we have:
side length of the cube = |-6| = 6 cm
Thus, its volume is:
[tex]V= (\rm side)^3 = 6^3 = 216 \: \rm cm^3[/tex]
Thus, the output for the considered rules are: Rule 1: -13, Rule 2: 36, Rule 3: -2, Rule 4: -2, Rule 5: π, Rule 6: 216 cubic cm.
Learn more about function here:
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