Answer:
f(x) = |x - 2| + 1
Step-by-step explanation:
When x = -2, then f(-2) = 5
The first function gives the relation equation as f(x) = |x| + 1
So, f(-2) = |-2| + 1 = 2 + 1 = 3 ≠ 5
{Since the definition of |x| is given by
|x| = x, when x ≥ 0 and |x| = - x, when x < 0}
Again, the second function gives the relation equation as f(x) = |x - 2|.
So, f(-2) = |-2 - 2| = |-4| = 4 ≠ 5
Now, the third function gives the relation equation as f(x) = |x - 2| - 1.
So, f(-2) = |-2 - 2| - 1 = |-4| - 1 = 4 - 1 = 3 ≠5
Again, the fourth function gives the relation equation as f(x) = |x - 2| + 1.
Hence, f(-2) = |-2 - 2| + 1 = |-4| + 1 = 4 + 1 = 5
Therefore, the fourth function f(x) = |x - 2| + 1 contains the given data table.
For further clarity we can check f(0) = 3, f(2) = 1, f(3) = 2 and f(5) = 4. (Answer)
