The only function that can be symmetric about the x-axis is the x-axis itself.
For each value of x a function, f(x), can have at most one value for f(x). Otherwise it is a mapping or relationship but not a function.
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Any point on the graph can be the center of a circle. If the center is on the x-axis, then the circle is symmetric with respect to the x-axis.
No, but they are symmetric with respect to a line parallel to the y-axis - which could be the y-axis itself.
When you with respect to the x-axis then this is like saying with reference to the x-axis. You are using the x-axis as a guide.
All y-values in the function are multiplied by -1. This function is 'flipped' over the x-axis.
An x-intercept is the point where a function intersects the x-axis on a Cartesian coordinate plane. For example, if the graph of a parabola is plotted and the graph intersects the x-axis on the coordinate plane, the point(s) where the graph intersects the x-axis are the x-intercepts for that function.