The graph of a function f(x) passes through the following points:
(0,-2), (1,0),(-1,0)
Which of the following could be f(x)?
A. O f(x) = 2sqrtx-2
B. O f(x) = -2x-2
C. O f(x) = 2x-2
D. O f(x) = 2x^2-2
To determine which of the given functions could be f(x), we need to check if they pass through the given points (0,-2), (1,0), and (-1,0).
Let's test each function with the given points.
A. f(x) = 2√x - 2
f(0) = 2√0 - 2 = -2 ✓
f(1) = 2√1 - 2 = 0 ✓
f(-1) = 2√(-1) - 2 = 2i - 2 ≠ 0 (Does not pass through (-1,0))
B. f(x) = -2x - 2
f(0) = -2(0) - 2 = -2 ✓
f(1) = -2(1) - 2 = -4 (Does not pass through (1,0))
f(-1) = 2(1) - 2 = 0 ✓
C. f(x) = 2x - 2
f(0) = 2(0) - 2 = -2 ✓
f(1) = 2(1) - 2 = 0 ✓
f(-1) = 2(-1) - 2 = -4 (Does not pass through (-1,0))
D. f(x) = 2x^2 - 2
f(0) = 2(0)^2 - 2 = -2 ✓
f(1) = 2(1)^2 - 2 = 0 ✓
f(-1) = 2(-1)^2 - 2 = 0 (Does not pass through (-1,0))
Therefore, the function that satisfies all the given points is:
B. f(x) = -2x - 2