To find the child's weight at birth, you would evaluate the function \( f(x) \) at the time \( x = 0 \) months (which represents birth).
Given the function:
\[ f(x) = 0.5x + 7.8 \]
We calculate \( f(0) \):
\[ f(0) = 0.5(0) + 7.8 = 0 + 7.8 = 7.8 \]
Therefore, the child's weight at birth was 7.8 lbs.