Write a piecewise function for the graph.

Similar to Modulus, but It's separated.

Since both are separated, that means - they are both linear function.

The range is greater than all negative numbers. That means y ≥ 0

( 1 ) For the blue graph,

y = -x-3  {y ≥ 0} Blue Graph Answer

-x-3=0

-x=3

x=-3

We can clearly see that the slope is -1.

And intercept x-axis at (-3,0)

( 2 ) For the red graph.

y = 2x+6 { y ≥ 0} Red Graph Answer

Notice that the slope is 2.

And intercept x-axis at (-3,0)

Also intercept y-axis at (0,6)

2x+6=0

2x=-6

x=-3

Only linear function with given y ≥ 0 can draw that. (Only separated graph.)