Question

\a\ between 0 and 1
if \a\ is between 0 and 1, describe the effect that \a\ has on the
child graph.

Explanation:

In the context of function transformations (specifically vertical stretches/compressions), when a function \( y = a \cdot f(x) \) has \( 0 < a < 1 \), the graph of \( y = f(x) \) (the parent graph) undergoes a vertical compression. Looking at the given graphs, the "child graph" (the darker, less tall/wide - in terms of amplitude - graph) compared to the parent (the lighter, more "stretched" graph) shows that the vertical distances from the x - axis (amplitudes) are reduced. So, when \( a \) is between 0 and 1, it vertically compresses the parent graph to form the child graph, making the child graph shorter (in terms of amplitude) than the parent graph.

Answer:

When \( 0 < a < 1 \), the value of \( a \) vertically compresses the parent graph to obtain the child graph. This means the child graph has a smaller amplitude (is "shorter" in terms of its vertical extent from the x - axis) compared to the parent graph.