Question

use the graph of ( y = f(x) ) to graph the function ( g(x)=f(-x) ).

Explanation:

Step1: Understand the transformation

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

Step2: Reflect the points

For the graph of \(y = f(x)\), if we have points \((x,y)\) on \(y = f(x)\), then the points on \(y = f(-x)\) will be \((-x,y)\).
The original graph of \(y = f(x)\) has endpoints at \(x=-2\), \(x = 0\), \(x=2\) (assuming the horizontal line segment). After applying the transformation \(g(x)=f(-x)\), the \(x\) - coordinates of the endpoints change their signs. The new endpoints will be at \(x = 2\), \(x=0\), \(x=- 2\) while the \(y\) - coordinate remains \(y = 4\) (since \(f(x)\) and \(f(-x)\) have the same \(y\) - value for a given \(|x|\)).

Answer:

Graph a horizontal line segment with \(y = 4\) from \(x=-2\) to \(x = 2\) (reflected about the \(y\) - axis compared to the original \(y = f(x)\) graph).