if f(x) is an even function, which statement about the graph of f(x) must be true? it has rotational…

if f(x) is an even function, which statement about the graph of f(x) must be true? it has rotational symmetry about the origin. it has line symmetry about the line y = x. it has line symmetry about the y - axis. it has line symmetry about the x - axis.

if f(x) is an even function, which statement about the graph of f(x) must be true? it has rotational symmetry about the origin. it has line symmetry about the line y = x. it has line symmetry about the y - axis. it has line symmetry about the x - axis.

Answer

Brief Explanations:

By definition, an even function satisfies (f(x)=f( - x)) for all (x) in its domain. This means that for every point ((x,y)) on the graph of (y = f(x)), the point ((-x,y)) is also on the graph. Geometrically, this represents line - symmetry about the (y) - axis. Rotational symmetry about the origin is a property of odd functions ((f(-x)=-f(x))). Symmetry about (y = x) is related to inverse functions. Symmetry about the (x) - axis is not a property of functions (since a function passes the vertical line test).

Answer:

C. It has line symmetry about the y - axis.