Identify the function that contains the data in the following table:

x -2 0 2 3 5
f(x) 3 1 -1 0 2

a. f(x) = |x - 2|
b. f(x) = |x - 2| - 1
c. f(x) = |x| + 1
d. f(x) = |x - 2| + 1

Option D is correct. f(x) = |x - 2| + 1

Step-by-step explanation:

Option A : f(x) = |x| + 1  INCORRECT

x = -2

we get, f(-2) = |-2| + 1 = 2 + 1 = 3 ≠ 5

⇒f(-2) is not equal to given value of f(-2).

Thus, This is not function of given data.

Option B f(x) = | x-2 |  INCORRECT

put, x = -2

we get, f(-2) = |-2 - 2|  = |-4| = 4 ≠ 5

⇒f(-2) is not equal to given value of f(-2).

Thus, This is not function of given data.  

Option C : f(x) = | x-2 | - 1  INCORRECT

put, x = -2

we get, f(-2) = |-2 - 2| - 1  = |-4| - 1 = 4 - 1 = 3 ≠ 5

⇒f(-2) is not equal to given value of f(-2).

Thus, This is not function of given data.  

Option D : f(x) = | x-2 | + 1  CORRECT

x = -2

f(-2) = |-2 - 2| + 1  = |-4| + 1 = 4 + 1 = 5

⇒f(-2) is equal to given value of f (-2).

x = 0

(0) = |0 - 2| + 1  = |-2| + 1 = 2 + 1 = 3

⇒f(0) is equal to given value of f (0).

x = 2

f(2) = |2-2| +1  = |0| + 1 = 0 + 1 = 1

⇒f(2) is equal to given value of f(2).

x = 3

we get, f(3) = |3-2| + 1  = |1| + 1 = 1 + 1 = 2

⇒f(3) is equal to given value of f(3).

x = 5

f(5) = |5 - 2| + 1  = |3| + 1 = 3 + 1 = 4

⇒f(5) is equal to given value of f(5).  

Therefore, Option D is correct.

step-by-step explanation: