Q&A for How to Tell if a Function Is Even or Odd

In the context of a piecewise function, continuity is achieved when, from both the right and left approaches, the function values (f of X or Y) coincide at a specific X value. In simpler terms, the functions smoothly connect, and there is mutual agreement that a particular X value yields the same result for both functions. However, the differentiability of the piecewise function is contingent on whether the derivatives concur in terms of the values approached from both sides.

Typically, functions are classified as even or odd according to how they behave on the X-axis and how their polynomial values are parsed. However, if a function represents a constant, it might not be regarded as even or odd. For instance, when Y equals 4, the graph forms a horizontal line at that point, passing the vertical line test and producing a different Y result for every X input. A constant function such as Y = 4 is neither even nor odd because it does not intersect the X-axis, even though it has no repeated Y values for any X input. This difference results from the function not exhibiting symmetry either about the origin (odd) or about the Y-axis (even).

It is neither. A quick way to verify that is to evaluate G (1) = 2 and G (-1)= 0.

It's even, since f(x) (which equals 4) = f(-x) (which equals -4) and an even function is when f(x) = f(-x) an an odd function is when the statement above does not hold.

It is even if Log (x-3) = Log (3-x) and odd if not. An even function is when f(x) = f(-x) and an odd function is when the aforementioned statement is not true.

This is neither even nor odd because it does not meet either of two requirements to be even or odd.

It's even. x^6 is even whether x is even or odd. The same is true of x^4 (or x raised to any even power). Subtracting an even number from another even number yields an even number.