Can someone please help me with this please please 😯
An even function is symmetrical about the origin(true or false )
To determine whether an even function is symmetrical about the origin or not, we can look at its definition and properties.
An even function is defined as a function where f(x) = f(-x) for all x in its domain. In other words, if you reflect the graph of an even function across the y-axis, it will match the original graph.
To check if an even function is symmetrical about the origin, we need to examine whether f(x) = f(-x) holds for all values of x, including x = 0.
Here's how you can determine if an even function is symmetrical about the origin:
1. Start with the given function and substitute -x for x:
f(-x) = f(x)
2. Simplify the equation by comparing the two sides and checking if they are equal.
- If the equation holds true for all x values, including x = 0, then the given function is symmetrical about the origin, and the statement "An even function is symmetrical about the origin" is true.
- If the equation does not hold true for all x values, including x = 0, then the given function is not symmetrical about the origin, and the statement is false.
By following these steps and comparing f(x) with f(-x), you will be able to determine if an even function is symmetrical about the origin or not.