Is there a function whose graph is symmetric with respect to the x-axis? Explain.

Is there a function whose graph is symmetric with respect to the x-axis.

A symmetric function is a function in several variable which remains unchanged for any permutation of the variables.

$f\left(x\right)=-f\left(x\right)$

If a graph does not change when reflected over a line or rotated around a point, the graph is symmetric with respect to that line or point.

The above graph is symmetric with respect to the x-axis (y = 0).

Let us consider some points from the graph (0, 2), (1, 3), (3, 4)... are the points on the graph.

Also the points (0, -2), (1, -3), (3, -4)... are also on the graph.

When we reflect the green graph about the x-axis x values are never change.

Note that if (x, y)is a point on the graph, then(x, - y) is also a point on the graph.

Yes, there is a function whose graph is symmetric with respect to the x-axis.