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)?

[] f(x)=-2x+2
[] f(x)=2x+2
[] f(x)=-2x^2+2
[] f(x)=-2/x+2

Answer 1

By checking which of the functions passes through the three given points, we can eliminate them accordingly:

1. f(x)=-2x+2
- f(0) = -2(0) + 2 = 2
- f(1) = -2(1) + 2 = 0
- f(-1) = -2(-1) + 2 = 4
This function does not pass through the points (1,0) and (-1,0), so it is not a valid solution.

2. f(x)=2x+2
- f(0) = 2(0) + 2 = 2
- f(1) = 2(1) + 2 = 4
- f(-1) = 2(-1) + 2 = 0
This function does not pass through the point (0,2), so it is not a valid solution.

3. 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
This function passes through all the given points, and hence could be f(x).

4. f(x)=-2/x+2
- f(0) = -2/0 + 2
Since division by 0 is undefined, this function is not valid.

Therefore, the function f(x)=-2x^2+2 is the only one that passes through the points (0,2), (1,0), and (-1,0).