Question

use the graph of ( y = f(x) ) to graph the function ( g(x)=f(x)-2 ) choose the correct graph of ( g ) below.

Explanation:

Step1: Vertical translation rule

For a function \(y = f(x)\), the transformation \(y=f(x)-k\) (\(k>0\)) shifts the graph of \(y = f(x)\) down by \(k\) units. Here \(k = 2\).

Step2: Analyze the original graph

The original graph \(y = f(x)\) has a horizontal line segment. Let's assume some points on \(y=f(x)\). For example, if we consider a general point \((x,y)\) on \(y = f(x)\), after the transformation \(g(x)=f(x)-2\), the new point is \((x,y - 2)\).

Answer:

Assuming the original graph \(y = f(x)\) (the left - hand side graph) has a horizontal line at \(y=-3\) (by looking at the grid). After applying \(g(x)=f(x)-2\) (shifting down 2 units), the new \(y\) - value of the horizontal line is \(y=-3-2=-5\). So the correct graph is C.