Question

symmetry: x - axis y - axis origin none of these graph 1 symmetry: x - axis y - axis origin none of these graph 2 symmetry: x - axis y - axis origin none of these graph 3

Explanation:

Step1: Recall symmetry definitions

• x - axis symmetry: If for every point \((x,y)\) on the graph, the point \((x, - y)\) is also on the graph.
• y - axis symmetry: If for every point \((x,y)\) on the graph, the point \((-x,y)\) is also on the graph.
• origin symmetry: If for every point \((x,y)\) on the graph, the point \((-x,-y)\) is also on the graph.

Step2: Analyze Graph 1

• If we take a point \((x,y)\) on the graph, \((x, - y)\) is not on the graph (no x - axis symmetry), \((-x,y)\) is not on the graph (no y - axis symmetry), and \((-x,-y)\) is not on the graph (no origin symmetry). So the symmetry of Graph 1 is none of these.

Step3: Analyze Graph 2

• For a circle centered at the origin, if \((x,y)\) is on the circle, then \((x, - y)\) (x - axis symmetry), \((-x,y)\) (y - axis symmetry) and \((-x,-y)\) (origin symmetry) are also on the circle.

Step4: Analyze Graph 3

• If \((x,y)\) is on the graph, then \((-x,y)\) is also on the graph (y - axis symmetry), but \((x, - y)\) and \((-x,-y)\) are not on the graph.

Answer:

Graph 1: none of these
Graph 2: x - axis, y - axis, origin
Graph 3: y - axis