How do i graph this function?

Question

f(x)={6-x, x<3
     =x+1, x>3

Answer 1

The peicewise function

Since the function has two pieces ,

The break between the two functions at x = 3

Choose random values for x and find the corresponding values for y.

The linear function f(x) = 6 - x , x < 3

x	y = 6 - x	(x, y)
-3	y = 6 - (-3) = 9	(- 3, 9)
-2	y = 6 - (-2) = 8	(-2,  8)
-1	y = 6 - (-1) = 7	(-1, 7)
0	y = 6 - (0) = 6	(0, 6)
1	y = 6 - (1) = 5	(1, 5)
2	y = 6 - (2) = 4	(2, 4)

The linear function f(x) =  x + 1 , x > 3

x	y = x + 1	(x, y)
4	y = 4 + 1 = 5	(4, 5)
5	y = 5 + 1 = 6	(5,  6)
6	y = 6 + 1 = 7	(6, 7)
7	y = 7 + 1 = 8	(7, 8)

Graph

Draw the coordinate plane.

Plot the points found in the table and connect the points.