Identify the function that contains the data in the following table: x     -2         0         2         3         5     f(x)     5         3         1         2         4     f(x) = |x| + 1 f(x) = |x - 2| f(x) = |x - 2| - 1 f(x) = |x - 2| + 1

Answer:f(x) = |x - 2| + 1Step-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)