Question

assume that the following graph has the given type of symmetry.
x - axis symmetry
complete the graph of the equation.

Explanation:

Step1: Recall x - axis symmetry rule

For a graph with x - axis symmetry, if a point \((x,y)\) is on the graph, then the point \((x, - y)\) is also on the graph.

Step2: Identify existing points

First, identify the key points on the given part of the graph. The starting point (the black dot) is at \((5,0)\) (assuming the x - coordinate of the dot is 5, since it's between 4 and 6, let's say 5 for simplicity, and y = 0). Then, for the curve above the x - axis, take a general point \((x,y)\) where \(x\geq5\) and \(y>0\).

Step3: Find symmetric points

For each point \((x,y)\) on the given curve (above the x - axis), plot the point \((x, - y)\) below the x - axis. The point \((5,0)\) is on the x - axis, so its symmetric point is itself (since \(y = 0\), \(-y=0\)). For other points, say if we have a point \((6,1)\) on the given curve, its symmetric point will be \((6, - 1)\); if we have a point \((8,2)\), its symmetric point will be \((8, - 2)\), and so on. We then draw the curve below the x - axis that is the mirror image of the curve above the x - axis with respect to the x - axis.

Answer:

To complete the graph with x - axis symmetry, for every point \((x,y)\) on the given upper part of the graph (where \(x\geq5\) and \(y\geq0\)), plot the point \((x, - y)\) below the x - axis. The point at \((5,0)\) remains, and the curve below the x - axis is the mirror reflection of the curve above the x - axis across the x - axis. So the completed graph will have a curve above the x - axis (as given) and a curve below the x - axis such that for each \(x\) (where the original curve is defined), the \(y\) - coordinate of the lower curve is the negative of the \(y\) - coordinate of the upper curve.