Afunction, h(x), is defined as shown.

h(x) =
which graph represents h(x)?

given: for the given function h(x), we have given four conditions  

(i) h(x) = (x ÷4) - 4   when x ≤ 0  

here, if x = 0, -1 , -2, -3, -4 then h(x) = -4, -4.25, -4.50, -4.75, -5  

from the above data, it represents the bottom line of the 2nd graph. (ii)   h(x) = (x ÷3) - 3   when   0< x ≤ 3  

here, if x = 1, 2, 3   then h(x) = - 2.7, - 2.3, - 2.0  

from the above data, it represents the second last bottom line of the 2nd graph.

(iii) h(x) = (x ÷2) - 2   when   x ≥ 4  

here, if x = 4, 5, 6, 7 h(x) = 0, 0.5, 1.0,  

from the above data, it represents the top line of the 2nd graph.  

hence, the correct representation of the given function will be the second graph.