Identify the function that contains the data

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

Step-by-step explanation:

Function which satisfy the given data is our Ans.

So, we check for all functions.

Option A : f(x) = |x| + 1

put, 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 |

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

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

put, x = -2

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

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

put, x = 0

we get, f( 0 ) = | 0 - 2 | + 1  = | -2 | + 1 = 2 + 1 = 3

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

put, x = 2

we get, f( 2 ) = | 2 - 2 | + 1  = | 0 | + 1 = 0 + 1 = 1

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

put, x = 3

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

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

put, x = 5

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

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

Thus, This is function of given data.  

Therefore, Option D is correct.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

thats not a system of equations, that is a solution