Question

which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?vertical translationhorizontal translationreflection over the x-axisreflection over the y-axis

Answer 1

The type of transformation that preserves the symmetry is Vertical translation.

For instance, a parabola is still symmetric about the y-axis if you move it up. It loses its symmetry if you move it to the left or right. Reflection keeps both even and odd functions symmetrical.

What is the difference between even and odd function ?

The symmetry of a function is described using the terms even and odd. On a graph, an even function is symmetric about the y-axis. An odd function has symmetric behavior around a graph's origin $(0, 0)$. This means that if you rotate an odd function 180 degrees around the origin, the function you started with will still exist.

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