A function assigns the values. The correct option is C, f(x)=2x².
A function assigns the value of each element of one set to the other specific element of another set.
Given that the table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long. Now, the function that can represent this table can be found by substituting the values in the function and checking if the two sides are equal or not.
A.) f(x)= x²+2x
f(1) should be equal to 2.
f(x)= x²+2x
f(1)= 1²+2(1) = 3
Thus, this is not the correct function.
B.) f(x)= x²/2
f(1) should be equal to 2.
f(x)= x²/2
f(1)= 1²/2 = 0.5
Thus, this is not the correct function.
C.) f(x)=2x²
f(1) should be equal to 2.
f(x)=2x²
f(1)= 2(1)² = 2
Also, f(2) should be equal to 8.
f(x)=2x²
f(1)= 2(2)² = 8
Thus, this is the correct function.
D.) f(x)=2x
f(1) should be equal to 2.
f(x)=2x
f(1)= 2(1) = 2
Also, f(2) should be equal to 8.
f(x)=2x
f(1)= 2(2) = 4
Thus, this is the correct function.
Hence, the correct function that represents the area of the box is f(x)=2x².
The complete question is,
Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long.
x 1 2 3 4 5
f(x) 2 8 18 32 50
A.) f(x)= x²+2x
B.) f(x)= x²/2
C.) f(x)=2x²
D.) f(x)=2x
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