Answer to: Prove that the graph of an odd function is the same when reflected across the x axis as it is when reflected across the y axis. By...
A function is odd if −f(x) = f(−x), for all x. The graph of an odd function will be symmetrical about the origin. For example, f(x) = x3 is odd. That is, the function on one side of x-axis is sign inverted with respect to the other side or graphically, symmetric ...
Learn what an odd function is and see examples. Understand the graphs of the odd function and the symmetry of the odd function in the graph with...
The graph of an even function is symmetric with respect to the y-axis. The graph of an odd function is symmetric with respect to the origin. The graph of an even function remains the same after reflection about the y-axis. The graph of an odd function is at the same distance from the...
解析 Recall that an odd function is symmetric with respect to the origin (versus an even function which is symmetric with respect to the y-axis.) Reflecting the given part of the function over the origin result in the following graph:
Odd and Even Functions: The graph of a function can be the basis to determine if the function is odd, even, or neither of the two. This can be determined by identifying the symmetry of the graph. Symmetry plays an important role in deter...
If a function is an odd function, its graph is symmetrical about the origin, that is, f(–x) = –f(x). Use the multiplicities of the zeros to determine the behavior of the polynomial at the x-intercepts. Determine the end behavior by examining the leading term. Use the end behavior ...
The highest exponent on the variable is 5, which is odd, so the function is odd. This means that the function values tend towards opposite signs of ♾ as x goes to opposite signs of ♾. •f(x) approaches ♾ as x approaches -♾ TRUE An odd function which ha...
14. Suppose that f(x)is an odd function defined in R and its graph is symmetric with respect to the line x=1,and f(x)=x for 0≤x≤1.Then the expression of f(x)is ( ) (A)1 f(x)= \( (matrix) x-4k+1 ≤q x ≤q 4k+ -x+2-4k 4k+1...
In mathematics, an odd function is a function such that when you evaluate the function to a negative input, the result is equal to the negative of the function evaluated at the corresponding positive value of the negative input, i.e. {eq...