解析 C。奇函数的图像关于原点对称。选项 A“x-axis”偶函数图像关于 y 轴对称时可能与 x 轴有特殊关系,但奇函数不是。选项 B“y-axis”偶函数图像关于 y 轴对称,奇函数不是。选项 D“line y=x”反函数图像与原函数图像关于 y=x 对称,与奇函数无关。
The terms even and odd are used to describe a function’s symmetry. An even function is symmetric around a graph’s y-axis. An odd function is symmetric about the graph’s origin (0,0). This means that rotating an odd function 180 degrees about the origin will give you the same ...
(–x) =–f(x), then the functionf(x) is said to be odd. For example,y= cosxandy=x2are even functions, andy= sinx, y=x3are odd functions. The graph of an even function is symmetric with respect to they-axis, and the graph of an odd function is symmetric with respect to the ...
A functionfisoddif for anyxin the domain offwe havef−x=−fx. Note that this means that thedomainoffmust be symmetric about 0, since−xmust be in the domain wheneverxis. An odd function is symmetric with respect to the origin. Draw the part of a function either to the le...
An odd function is symmetric about the origin. [For example, is an odd function.] Note: Symmetry about the origin = a reflection in the y-axis + a reflection in the x-axis Evens and Odds – Practice Determine whether each of the functions below is even, odd or neither. Justify your ...
An odd function is a function where f(-x) = -f(x), meaning that it is symmetric about the origin. An even function is a function where f(-x) = f(x), meaning that it is symmetric about the y-axis. In other words, an odd function has rotational symmetry of 180 degrees and an...
What is an example of determining if a function is even, odd, or neither?Determine algebraically whether f (x) = −3x2 + 4 is even, odd, or neither.If I graph this, I will see that this is "symmetric about the y-axis"; in other words, whatever the graph is doing on one ...
A function f(x) is even if f(-x) = f(x), for all values of x in D(f) and it is odd if f(-x) = -f(x), for all values of x. The graph even function is symmteric with respect to the y-axis and the graph of an odd function is symmetric about the origin. A real-va...
The function g(x) = x3 - 3x is symmetric about the origin and is thus an odd function.Stated another way, functions are even if changing x to -x does not change The value of the function.EVEN FUNCTION: f(x) = x2 - 18f(-x) = (-x)2 - 18 = x2 - 18 Since f(-x) = f...
A half range Fourier series is calculated over half of the period of the function, while a full range Fourier series is calculated over the entire period.3. What is the difference between an odd and even function? An odd function is symmetric about the origin, meaning that f(-x) = -f...