91Ó°ÊÓ

The absolute value of a number represents its distance from 0 on the number line. Hence, the absolute value of a positive number is itself, and for a negative number, it is the negation of the number. For example, \(|3| = 3\) and \(|-3| = 3\).

We will rewrite the given function, \(g(x) = |x| - 4\), as a piecewise function that does not involve absolute value bars. Since the rule for the absolute value "|x|" is x, if x≥0; and -x, if x<0, we can use these conditions to rewrite the given function. $$ g(x) = \begin{cases} x - 4, & \text{if}\ x \geq 0 \\ -x - 4, & \text{if}\ x < 0 \end{cases} $$

Now, we will graph the function, by first plotting the points for the two cases when \(x \geq 0\) and \(x < 0\) separately. Case 1: \(g(x) = x - 4\) if \(x \geq 0\). - Choose values of x greater than or equal to 0, and find their corresponding y-values using the equation \(g(x)=x-4\). For example, we can choose \(x=0, 1, 2, 3\) and obtain respective y-values of \(-4, -3, -2, -1\). - Plot these points on the graph: \((0, -4), (1, -3), (2, -2), (3,-1)\). - Connect these points with a straight line. Case 2: \(g(x) = -x - 4\) if \(x < 0\). - Choose values of x less than 0, and find their corresponding y-values using the equation \(g(x)=-x-4\). For example, we can choose \(x=-1, -2, -3, -4\) and obtain respective y-values of \(-3, -2, -1, 0\). - Plot these points on the graph: \((-1, -3), (-2, -2), (-3, -1),(-4, 0)\). - Connect these points with a straight line. After plotting both cases on the graph, you will observe that the final graph is a V-shaped graph.