Question on Functions

Question

x+1 for x [-1,1)
h(x) =  {         2 for x [-1,3)      }

                 -x+5 for [3,5]

and that h(x) = h(x+6) for all real values of x.

(i) Sketch the graph of y=h(x) for x [-1,11]

How do i sketch for values of x above 5  ? and what does h(x) = h(x+6) for all values of x mean ?
Because for values of x between -1 to 5, it does not equate to (x+6), so im confused.

Sorry this is my 1st time here and I couldnt find the inequality signs ><

Answer 1

The piecewise function

The function has 3 pieces.

x	y=x+1	(x, y)
-1	y=-1+1	(-1,0)
0	y=0+1=1	(0,1)

 

x	y=2	(x, y)
-1	y=2	(-1,2)
1	y=2	(1, 2)
2	y=2	(2, 2)

 

x	y=-x+5	(x, y)
3	y=-3+5	(3, 2)
4	y=-4+5	(4, 1)
5	y=-5+5	(5, 0)

 

Comments

Graph

1.Draw the coordinate plane.

2.Plot the points found in the table.

3.Connect the plotted points.

Answer 2

The piecewise function

And h(x) = h(x + 6) for all real values of x.

h(x) = x + 1

h(x + 6) = x + 6 + 1

h(x+ 6) = x + 7 for [-1, 1)

 

h(x+ 6) = 2 for [-1, 3)

 

h(x) = - x + 5

h(x + 6) = -(x + 6) + 5

= - x - 6 + 5

h(x + 6) = - x - 1 for [3, 5].