Question

use the graph of ( y = f(x) ) to graph the function ( g(x) = f(x) + 2 ). choose the correct graph of ( g ) below.
options: a, b, c, d (with corresponding graphs)

Explanation:

Step1: Identify transformation rule

The function $g(x)=f(x)+2$ is a vertical shift of $f(x)$ up by 2 units.

Step2: Apply shift to $f(x)$ points

Take the endpoints of the horizontal segment of $f(x)$: let the left endpoint be $(x_1, y_1)$ and right endpoint be $(x_2, y_2)$. For $g(x)$, these points become $(x_1, y_1+2)$ and $(x_2, y_2+2)$. From the given $f(x)$ graph, the segment is on $y=-2$, so shifting up 2 units moves it to $y=0$.

Answer:

Option C (the graph with the horizontal segment on the x-axis, shifted up 2 units from the original $f(x)$ segment)