y-axis Symmetry
even functions
The concept of y-axis symmetry is related to the symmetry of the graph of a function about the y-axis. It means that the graph is perfectly symmetrical when reflected about the y-axis, which is a vertical line passing through the origin of the coordinate plane.
To test if a function has y-axis symmetry, we can replace x by -x in the equation of the function. If the resulting expression is the same as the original equation, then the function is symmetric about the y-axis.
For example, let’s consider the function f(x) = x^2. If we replace x by -x, we get f(-x) = (-x)^2 = x^2. Since this is the same as the original equation of f(x), we can conclude that the graph of f(x) has y-axis symmetry.
In general, if a function is even, meaning f(-x) = f(x) for all x in the domain, then it has y-axis symmetry. Examples of even functions include f(x) = x^2 and f(x) = cos(x).
On the other hand, if a function is odd, meaning f(-x) = -f(x) for all x in the domain, then its graph has rotational symmetry about the origin but not y-axis symmetry. Examples of odd functions include f(x) = x^3 and f(x) = sin(x).
More Answers:
The Symmetry Of Odd Functions In MathematicsEven Functions In Mathematics: Definition, Examples, And Properties
Origin Symmetry In Math: How To Determine And Identify Symmetrical Objects