Question

when the value of (a) lies in between 0 and 1 in the equation (y = a|x - h| + k), the graph will be

• closer to the (y)-axis
• further from the (y)-axis

Explanation:

Identify the transformation parameter

The given equation is \(y = a|x - h| + k\), where \(a\) represents the vertical stretch or compression factor of the parent absolute value function \(y = |x|\).

Analyze the effect of the parameter value

When \(0 < a < 1\), the function undergoes a vertical compression (or vertical shrink). This means that for any given horizontal distance from the vertex, the vertical distance is smaller compared to the parent function \(y = |x|\).

Determine the geometric behavior of the graph

A vertical compression makes the V-shape of the absolute value graph wider (flatter). As the graph becomes wider, its branches open up more horizontally, moving further away from the vertical axis of symmetry (and thus further from the \(y\)-axis compared to a vertically stretched graph where \(a > 1\)).

Answer:

• closer to the \(y\)-axis
• further from the \(y\)-axis (Correct answer)