To compare the function \( a(x) = x - 1.5 \) to the parent function \( f(x) = x \), we need to analyze how the equation for \( a(x) \) modifies the behavior of the parent function \( f(x) \).
The parent function is \( f(x) = x \), which is a straight line passing through the origin with a slope of 1.
In the function \( a(x) = x - 1.5 \), the term \(-1.5\) indicates a vertical transformation. Specifically, since we are subtracting 1.5 from \( x \), this results in a vertical translation of the graph downward by 1.5 units.
Therefore, the correct interpretation is:
Vertical translation down 1.5 units.
The graph of \( a(x) \) will look the same as the graph of \( f(x) \), but it will be shifted downwards by 1.5 units.