Question

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. f(x)=-2sqrtx+2
B. f(x)=-2x+2
C. f(x)2x+2
D. f(x)=-2x^2+2

Answer 1

To determine which of the given functions could be f(x), we can substitute each of the given points into the functions and see which ones satisfy all the points.

Given points:
(0,2), (1,0),(-1,0)

A. f(x) = -2√x + 2
For x = 0: f(0) = -2√0 + 2 = 2 (Correct)
For x = 1: f(1) = -2√1 + 2 = 0 (Correct)
For x = -1: f(-1) = -2√(-1) + 2 = -2 + 2 = 0 (Correct)

B. f(x) = -2x + 2
For x = 0: f(0) = -2(0) + 2 = 2 (Incorrect, should be 2)
For x = 1: f(1) = -2(1) + 2 = 0 (Correct)
For x = -1: f(-1) = -2(-1) + 2 = 4 (Incorrect, should be 0)

C. f(x) = 2x + 2
For x = 0: f(0) = 2(0) + 2 = 2 (Correct)
For x = 1: f(1) = 2(1) + 2 = 4 (Incorrect, should be 0)
For x = -1: f(-1) = 2(-1) + 2 = 0 (Correct)

D. f(x) = -2x^2 + 2
For x = 0: f(0) = -2(0)^2 + 2 = 2 (Incorrect, should be 2)
For x = 1: f(1) = -2(1)^2 + 2 = 0 (Correct)
For x = -1: f(-1) = -2(-1)^2 + 2 = 0 (Correct)

Therefore, the function that could be f(x) based on the given points is D. f(x) = -2x^2 + 2.