Question

testing for symmetry graphically in exercises 23 and 24, test the graph for symmetry with respect to the given axis or the origin. 23. origin 24. y - axis

Explanation:

23.

Step1: Recall origin - symmetry rule

A graph is symmetric about the origin if for every point \((x,y)\) on the graph, the point \((-x,-y)\) is also on the graph.

Step2: Check points

For the point \((4,4)\) on the graph, the point \((- 4,-4)\) is also on the graph. For the point \((2,2)\), the point \((-2,-2)\) is on the graph, and for the point \((0,0)\), \((-0,-0)=(0,0)\) is on the graph.

Step1: Recall y - axis symmetry rule

A graph is symmetric about the \(y\) - axis if for every point \((x,y)\) on the graph, the point \((-x,y)\) is also on the graph.

Step2: Check points

For the point \((1,0)\) on the graph, the point \((-1,0)\) is not on the graph. For the point \((2, - 2)\), the point \((-2,-2)\) is on the graph, but since \((1,0)\) does not have its \(y\) - axis counterpart \((-1,0)\) on the graph.

Answer:

The graph is symmetric about the origin.

24.