Question

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

x	f(x)
-6	0
-5	2
-4	0
-3	-2

show your work here

draw button and coordinate plane with some pre - drawn points

Explanation:

Step1: Identify Coordinates

From the table, the points are \((-7, -2)\), \((-6, 0)\), \((-5, 2)\), \((-4, 0)\), \((-3, -2)\).

Step2: Plot Points

On the coordinate plane, mark each point:

• For \((-7, -2)\): Move 7 units left on x - axis, 2 units down on y - axis.
• For \((-6, 0)\): Move 6 units left on x - axis, 0 units (on x - axis).
• For \((-5, 2)\): Move 5 units left on x - axis, 2 units up on y - axis.
• For \((-4, 0)\): Move 4 units left on x - axis, 0 units (on x - axis).
• For \((-3, -2)\): Move 3 units left on x - axis, 2 units down on y - axis.

Step3: Connect Points

Since it's an absolute - value function, the graph should form a "V" - shape. Connect the plotted points in order. The vertex of this absolute - value function (the minimum point of the "V") can be found by looking at the symmetry. The x - values around which the y - values are symmetric: between \(x=-6\) (where \(y = 0\)) and \(x=-4\) (where \(y = 0\)), the mid - point of \(x=-6\) and \(x=-4\) is \(x=\frac{-6 + (-4)}{2}=-5\), and at \(x=-5\), \(y = 2\) is the maximum in this symmetric region? Wait, no, actually looking at the y - values: when \(x=-6\) and \(x=-4\), \(y = 0\); when \(x=-7\) and \(x=-3\), \(y=-2\); when \(x=-5\), \(y = 2\). So the graph is a "V" that opens downward? Wait, no, the standard absolute - value function \(y=\vert x\vert\) opens upward. But here, let's check the symmetry. The axis of symmetry is \(x=\frac{-7 + (-3)}{2}=\frac{-10}{2}=-5\)? Wait, \(x=-7\) and \(x=-3\) have \(y=-2\); \(x=-6\) and \(x=-4\) have \(y = 0\); \(x=-5\) has \(y = 2\). So the graph is a "V" with vertex at \((-5, 2)\) and opening downward? Wait, no, when we plot the points: \((-7,-2)\), \((-6,0)\), \((-5,2)\), \((-4,0)\), \((-3,-2)\). So starting from \((-7,-2)\), going up to \((-6,0)\), then to \((-5,2)\) (the peak), then down to \((-4,0)\), then to \((-3,-2)\). So it's a "V" - shape opening downward with vertex at \((-5, 2)\). Connect the points in this order to get the graph of the absolute - value function.

(Note: Since the drawing tool is available, after plotting the points, we can use the draw tool to connect them to form the correct graph.)

Answer:

The graph is formed by plotting the points \((-7, -2)\), \((-6, 0)\), \((-5, 2)\), \((-4, 0)\), \((-3, -2)\) and connecting them in a "V" - shape with vertex at \((-5, 2)\) (the graph should be drawn as per the plotted points and connected appropriately).