Let's break down the interpretation of the given notation step-by-step:
1. Understanding the Function Notation:
- The function notation [tex]\( v(s) \)[/tex] represents the volume of a cube as a function of its side length [tex]\( s \)[/tex].
- For a cube, the volume [tex]\( v \)[/tex] is given by the formula [tex]\( v = s^3 \)[/tex], where [tex]\( s \)[/tex] is the length of a side of the cube.
2. Interpreting [tex]\( v(2) = 8 \)[/tex]:
- Here, [tex]\( v(2) = 8 \)[/tex] means that when the side length [tex]\( s \)[/tex] of the cube is 2 feet, the volume [tex]\( v \)[/tex] of the cube is 8 cubic feet.
- This aligns with the formula [tex]\( v = s^3 \)[/tex]. For [tex]\( s = 2 \)[/tex] feet, the volume calculation would be [tex]\( 2^3 = 8 \)[/tex] cubic feet.
3. Matching the Interpretation to the Given Choices:
- Option A: "A cube with a volume of 2 cubic feet has side lengths of 8 feet."
- This option suggests the volume is 2 cubic feet, which does not match our interpretation of [tex]\( v(2) = 8 \)[/tex].
- Option B: "A cube with side lengths of 2 feet has a volume of 8 cubic feet."
- This directly matches [tex]\( v(2) = 8 \)[/tex], where a cube with side lengths of 2 feet indeed has a volume of 8 cubic feet.
- Option C: "2 sides of the cube have a total length of 8 feet."
- This option is unrelated to the volume and discusses lengths, which does not align with the function notation for volume.
- Option D: "2 of these cubes will have a total volume of 8 cubic feet."
- This option suggests that the total volume for 2 cubes is 8 cubic feet, which implies each cube would have a volume of 4 cubic feet. This does not match the given notation of [tex]\( v(2) = 8 \)[/tex].
4. Conclusion:
- The best interpretation of [tex]\( v(2) = 8 \)[/tex] aligns perfectly with choice B.
So, the best interpretation is:
B. A cube with side lengths of 2 feet has a volume of 8 cubic feet.
