Question

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

x	f(x)
-6	-7
-5	-6
-4	-5
-3	-6
-2	-7

show your work here

Explanation:

Step1: Identify key points

From the table, the points are \((-6, -7)\), \((-5, -6)\), \((-4, -5)\), \((-3, -6)\), \((-2, -7)\). Notice the symmetry around \(x = -4\) (since \(f(-6)=f(-2)= -7\), \(f(-5)=f(-3)= -6\), and \(f(-4)= -5\)). The vertex of the absolute - value function (the minimum point) is at \((-4, -5)\).

Step2: Plot the points

• For \(x=-6\), \(y = - 7\): Locate the point \((-6, -7)\) on the coordinate plane.
• For \(x=-5\), \(y = - 6\): Locate the point \((-5, -6)\) on the coordinate plane.
• For \(x=-4\), \(y = - 5\): Locate the point \((-4, -5)\) on the coordinate plane (this is the vertex).
• For \(x=-3\), \(y = - 6\): Locate the point \((-3, -6)\) on the coordinate plane.
• For \(x=-2\), \(y = - 7\): Locate the point \((-2, -7)\) on the coordinate plane.

Step3: Draw the graph

Since it's an absolute - value function, the graph should be a V - shaped graph. Connect the points in a way that forms a V with the vertex at \((-4, -5)\). The left side of the V (for \(x < - 4\)) goes from \((-4, -5)\) through \((-5, -6)\) to \((-6, -7)\), and the right side (for \(x>-4\)) goes from \((-4, -5)\) through \((-3, -6)\) to \((-2, -7)\).

Answer:

The graph is a V - shaped absolute - value graph with vertex at \((-4, -5)\) and passing through the points \((-6, -7)\), \((-5, -6)\), \((-3, -6)\), \((-2, -7)\) (plotted and connected as described in the steps).