Question

\a\ greater than 1
blue: parent graph
black: child graph

if \a\ is greater than 1, describe the effect that \a\ has on the child graph.

Explanation:

In the context of function transformations (specifically vertical stretches/compressions), when the coefficient \( a \) (in a function of the form \( y = a \cdot f(x) \)) is greater than 1, it represents a vertical stretch. Looking at the graphs, the black (child) graph is taller (has greater amplitude) than the blue (parent) graph. This means the \( y \)-values of the child graph are multiplied by \( a \) (where \( a>1 \)), so the graph is stretched vertically, making it narrower in terms of the "height" relative to the parent, or more precisely, each point \((x,y)\) on the parent graph becomes \((x, a\cdot y)\) on the child graph, leading to a vertical stretch (amplitude increase) when \( a > 1 \).

Answer:

When \( a>1 \), the child graph (black) is a vertical stretch of the parent graph (blue). This means the graph is stretched vertically, increasing its amplitude (the height from the midline to the peak/trough) compared to the parent graph. Each \( y \)-coordinate of a point on the parent graph is multiplied by \( a \) to get the corresponding \( y \)-coordinate on the child graph, making the graph taller (and narrower in terms of the vertical scaling effect on the shape's "height").