Question

graph the absolute value function represented by the table of values.

x	f(x)
-6	9
-5	6
-4	3
-3	6
-2	9

show your work here
draw

Explanation:

Step1: Identify Coordinates

From the table, the points are \((-6, 9)\), \((-5, 6)\), \((-4, 3)\), \((-3, 6)\), \((-2, 9)\).

Step2: Plot Points

On the coordinate plane, locate each \(x\)-value (horizontal axis) and corresponding \(f(x)\)-value (vertical axis). For example, at \(x = -6\), move 6 units left on the \(x\)-axis and 9 units up on the \(y\)-axis to plot \((-6, 9)\). Repeat for all points.

Step3: Connect Points

Since it's an absolute - value function, the graph should be a V - shape. The vertex here is at \(x=-4\) (where \(f(x)\) is minimum, \(f(-4) = 3\)). Connect the plotted points smoothly, forming two line segments: one from \((-6,9)\) to \((-4,3)\) and another from \((-4,3)\) to \((-2,9)\), extending the pattern if needed.

Answer:

The graph is plotted by marking the points \((-6, 9)\), \((-5, 6)\), \((-4, 3)\), \((-3, 6)\), \((-2, 9)\) on the coordinate plane and connecting them to form a V - shaped graph (absolute - value graph) with the vertex at \((-4, 3)\).