Carcass wrote:
If \(f(–0.5) = 0\), which of the following could be \(f(x)\)?
(A) \(2x + 2\)
(B) \(4x – 2\)
(C) \(4x^2 – 1\)
(D) \(x^2 – 1\)
(E) \((–x)^2 – 2.5\)
With function problems and variables in the choices, plugging in values is the most efficient tactic.
In this case, plug (-0.5) into each choice to see if it = 0 to meet the conditions of the problem:
(A) 2(-0.5) + 2 ≠ 0 | Eliminate
(B) 4(-0.5) + 4 ≠ 0 | Eliminate
(C) 4(-0.5)² + 1 = 0 | Keep
(D) (-0.5)² + 1 ≠ 0 | Eliminate
(E) (0.5)² -2.5 ≠ 0 | Eliminate
Only one choice matches the conditions of the problem, so select Choice C.