Hi,
The graph of g consists of two parts:
1. It is a straight line for 0 <= x < 2.
2. It is a horizontal line for 2 <= x < 4.
The given condition g(x) = g(x + 4) for all real values
of x means that the y-values at the points x and x + 4 are the
same. Therefore, the graph of g repeats itself with a period of 4
units.
For (i), we observe that g(5 + 4) = g(5) and g(1 + 4) =
g(1), and since x = 1 satisfies the first part of the graph, we
could use its rule to calculate g(1).
For (ii), we will sketch two and a half cycles of the
graph of g, i.e., 0 <= x < 4, 4 <= x < 8, 8 <= x
< 10, x = 10.
This question first appeared in the 2009 exam and it was
an atypical problem then.
Cheers,
Wen Shih