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The absolute value transforms a negative number into a positive number.
For example
Let z be a real number, then:
| z | It will always be a positive number.
This means that:
If z is a negative number, then:
| z | = -z
If z is a positive number, then:
| z | = z
This means that for the expression the expression y = 2 | x-3 | +5
When x-3 > 0 then:
| x-3 | = x-3
When x-3 < 0 then:
| x-3 | = - (x-3)
Then we can divide the expression into two functions f (x) and g (x).
f (x) = 2 (x-3) +5
f (x) = 2x-6 + 5
f (x) = 2x-1
For
g (x) = 2 (-x + 3) +5
g (x) = -2x + 6 + 5
g (x) -2x +11
For
(x-3) < 0
x < 3