Symmetric with respect to the x-axis
When a graph or shape is symmetric with respect to the x-axis, it means that if you were to fold the image along the x-axis, the two halves would perfectly overlap each other
When a graph or shape is symmetric with respect to the x-axis, it means that if you were to fold the image along the x-axis, the two halves would perfectly overlap each other.
To determine if a graph or shape is symmetric with respect to the x-axis, you need to check if the y-coordinates of points on one half are equal to the y-coordinates of the corresponding points on the other half when reflected across the x-axis.
For a function, you can test for symmetry by replacing y with -y in the equation and simplifying. If the resulting equation is equivalent to the original equation, then the function is symmetric with respect to the x-axis.
For example, let’s consider the equation of a function: y = x^2. To test for symmetry with respect to the x-axis, we replace y with -y:
-y = x^2.
We can simplify this equation to:
y = -x^2.
Since this equation is not equivalent to the original equation, y = x^2, the function is not symmetric with respect to the x-axis.
On the other hand, let’s consider the equation of another function: y = 3x + 2. Replacing y with -y, we get:
-y = 3x + 2.
Simplifying this equation, we have:
y = -3x – 2.
Since this equation is equivalent to the original equation, y = 3x + 2, the function is symmetric with respect to the x-axis.
In terms of shapes such as graphs or figures, you can also visually inspect if the shape appears to be symmetrical with respect to the x-axis. If the left half of the shape is a mirror image of the right half when reflected across the x-axis, then it is symmetric.
Overall, determining if a graph or shape is symmetric with respect to the x-axis involves either algebraic or visual analysis.
More Answers:
Understanding Decreasing Functions: A Guide to Math Concepts and ApplicationsFinding the Relative Maximum: Step-by-Step Guide Within a Given Interval [Mathematics]
Finding Relative Minima: A Step-by-Step Guide for Math Enthusiasts