Question

describe the transformation. the graph of f is a reflection in the followed by a translation 3 units of the graph of the parent

Explanation:

Step1: Analyze the reflection

The graph of the parent - function \(y = |x|\) has been reflected. By observing the orientation change, we can see that it is a reflection in the \(x\) - axis. When a function \(y = f(x)\) is reflected in the \(x\) - axis, the new function is \(y=-f(x)\). For \(y = |x|\), the reflected function is \(y=-|x|\).

Step2: Analyze the translation

After the reflection, the graph is translated 3 units down. The general rule for a vertical translation of a function \(y = g(x)\) by \(k\) units down is \(y=g(x)-k\). Since \(g(x)=-|x|\) and \(k = 3\), the final function is \(y=-|x|-3\).

Answer:

The graph of \(f\) is a reflection in the \(x\) - axis followed by a translation 3 units down of the graph of the parent.