Question

describe the transformation that must be applied to the graph of f(x) to obtain the graph of g(x). the graph of f(x) is a reflection in the y - axis of the graph of g(x). the graph of g(x) is a reflection in the y - axis of the graph of f(x). the graph of g(x) is a reflection in the x - axis of the graph of f(x). the graph of f(x) is a reflection in the x - axis of the graph of g(x).

Explanation:

When a graph \(y = f(x)\) is reflected in the \(y -\)axis, the transformation is \(y=f(-x)\). When reflected in the \(x -\)axis, the transformation is \(y = - f(x)\). Looking at the graphs of \(f(x)\) and \(g(x)\), we can see that for every point \((x,y)\) on \(f(x)\), the corresponding point on \(g(x)\) has the same \(y -\)coordinate but the opposite \(x -\)coordinate. This is the rule for a \(y -\)axis reflection.

Answer:

The graph of \(g(x)\) is a reflection in the \(y - axis\) of the graph of \(f(x)\).