CALCULUS AB Given g(x), name the piecewise function and graph:
g(x)+1
g(x-1)
-g(x)
2g(x)
-g(x-1)
|g(x)|

A piecewise function is one that has different operations, depending on the values of the input

The piecewise function is;

Reason:

The general form of the absolute value function is presented as follows;

The function given in the graph are;

Domain; -5 ≤ x < 0

Function;  

Domain; 0 < x ≤ 2

Points on the graph are;

(0, -2), and (2, 2)

Slope = (2 - (-2))/(2 - 0) = 2

g(x) - (-2) = 2·(x - 0)

∴ Function; g(x)  = 2·x - 2

Domain; 2 ≤ x ≤ 5

Function; g(x) = 2

Therefore, we have the following piecewise function;

Learn more about piecewise functions here: