Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What property describes an odd function?

It is symmetric with respect to the y-axis
It satisfies f(x) = f(-x)
It has an even degree
It satisfies f(x) = -f(-x)

The correct answer is: It satisfies f(x) = -f(-x)

An odd function is defined by the property that it satisfies the equation f(x) = -f(-x). This means that for any input x, if you take the negative of that input, the output will also be the negative of the original output. This creates symmetry about the origin when you graph the function, indicating that if you were to rotate the graph 180 degrees around the origin, it would overlap with itself. The other properties listed in the choices refer to different types of symmetry or characteristics of functions. For instance, symmetric with respect to the y-axis pertains to even functions, which are defined by the property f(x) = f(-x). The reference to even degree relates to polynomial functions where the highest degree of x is an even number, often leading to even functions. The association between even degree and symmetry is significant but specific to even functions, not odd ones. Thus, the distinguishing criterion for odd functions is that their output changes sign when the input is replaced with its negative, accurately captured by the property f(x) = -f(-x).