The problem asks to graph the function $g(x) = |x| - 8$.

1. Problem Description

The problem asks to graph the function $g(x) = |x| - 8$.

2. Solution Steps

The function $g(x) = |x| - 8$ is an absolute value function.

The absolute value function $y = |x|$ has a V-shape, with its vertex at the origin (0, 0). The arms of the V extend upwards and outwards from the origin, with slopes of -1 for $x < 0$ and +1 for $x > 0$.

The function $g(x) = |x| - 8$ is a vertical translation of the function $y = |x|$. Specifically, it shifts the graph of $y = |x|$ downwards by 8 units.

Therefore, the vertex of the graph of $g(x) = |x| - 8$ is at (0, -8). The arms of the V still extend outwards with slopes of -1 and +

1.

To sketch the graph, we can consider a few points.

When $x = 0$, $g(0) = |0| - 8 = -8$.

When $x = 1$, $g(1) = |1| - 8 = 1 - 8 = -7$.

When $x = -1$, $g(-1) = |-1| - 8 = 1 - 8 = -7$.

When $x = 8$, $g(8) = |8| - 8 = 8 - 8 = 0$.

When $x = -8$, $g(-8) = |-8| - 8 = 8 - 8 = 0$.

3. Final Answer

$g(x) = |x| - 8$