The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x). Learn how to plot an odd function graph and also check out the solved examples, practice questions
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...
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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...
1. A function whose graph is symmetric with respect to the y-axis is an even function. In other words, the points (x, y) and (-x, y) are both on the graph. 2. A function whose graph is symmetric with respect to the origin is an odd function. In other words, the points (x,...
Let's look at a couple examples.Example 1: Determine if the function f(x) = x6 + 4x2 - 1 is even, odd or neither then graph the function and describe the symmetry.Step 1: Replace f(x) with f(-x) and simplify the function. Original function: f(x) = x6 + 4x2 - 1 Substitu...
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...
Because the sine function is an odd function, for a negative number u, sin(2u) = -2sin(u)cos(u). True False Explain. Determine whether the statement is true or false. The graph of y = -cos x is a reflection of the graph of y...
Examples are all odd-powered functions (f(x)=x^n with n an odd integer ), the trigonometric functions sin x, tan x, and csc x, and the rational function x/(1-x2). The graph of an odd function has an S-shaped symmetry about the origin, that is, the graph will look the same ...
The endpoints of a function may be the lowest or highest points (thus the absolute, not relative extrema); these are called the endpoint extrema. Here is a graph that shows some examples of absolute/relative extrema; note also the endpoint extrema points: We discuss how the extrema of ...