which functions are symmetric about the y - axis? check all of the boxes that apply.
which functions are symmetric about the y - axis? check all of the boxes that apply.
Answer
Explanation:
Step1: Recall y - axis symmetry property
A function is symmetric about the y - axis if for every point (x, y) on the graph, the point (-x, y) is also on the graph. Visually, the left - hand side of the y - axis is a mirror image of the right - hand side.
Step2: Analyze each graph
For the first graph, if we take a point on the right - hand side of the y - axis and reflect it across the y - axis, the corresponding point is on the graph. So it is symmetric about the y - axis. For the second graph, if we take a point on the right - hand side of the y - axis and reflect it across the y - axis, the corresponding point is not on the graph. So it is not symmetric about the y - axis. For the third graph, if we take a point on the right - hand side of the y - axis and reflect it across the y - axis, the corresponding point is on the graph. So it is symmetric about the y - axis.
Answer:
The first and the third functions (graphs) are symmetric about the y - axis.