Considering the definition of the absolute value of a number, the values are A(3)= 2, A(0)= 3 and A(-2)= 5.
Absolute value of a real number
The absolute value of a real number is its magnitude, regardless of the sign that precedes it.
That is, the absolute value of an integer equals its numerical value regardless of the sign. It is represented by vertical bars around the number: |x|
The absolute value of a number, in other words, is the value that results from eliminating the sign corresponding to it:
- When the value of x is positive, the absolute value results in the same number.
- When the number is negative, the absolute value results in the opposite number (a number that has the same value, but opposite sign).
- When the number is zero, |0| = 0.
This case
The absolute value function can be defined as A(x)=|x−2|+1. Replacing x by the corresponding values and solving, you obtain:
A(3)= |3−2|+1= |1| +1= 1+1 → A(3)= 2
A(0)= |0−2|+1= |-2|+1= 2+1= 3 → A(0)= 3
A(−2)= |-2−2|+1= |-4| +1= 4+1= 5 → A(-2)= 5
In summary, the values are A(3)= 2, A(0)= 3 and A(-2)= 5.
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