Answer:
False.
To determine if the sequence 2, 8, 18, 32, ... can be represented by the explicit function f(x) = 2x^2, we can test whether this formula generates the terms of the sequence.
When x = 1, we have f(1) = 2(1)^2 = 2, which is the first term of the sequence.
When x = 2, we have f(2) = 2(2)^2 = 8, which is the second term of the sequence.
However, when x = 3, we have f(3) = 2(3)^2 = 18, which is the third term of the sequence. But the fourth term of the sequence is 32, which is not generated by the formula f(x) = 2x^2 when x = 4.
Therefore, the sequences 2, 8, 18, 32, ... cannot be represented by the explicit function f(x) = 2x^2.