If you mean the y values, then no it doesn't mean it's always positive.
Consider something like y = 3x+2 which is a linear function. It graphs a straight line through the two points (0,2) and (1,5)
If you plugged a number like x = -10, then...
y = 3x+2
y = 3*(-10)+2
y = -30 + 2
y = -28
So we see that y isn't positive here.