Determine whether F(x) is symmetric with respect to the y-axis or the origin.
To determine whether a function F(x) is symmetric with respect to the y-axis or the origin, we need to check for a specific condition
To determine whether a function F(x) is symmetric with respect to the y-axis or the origin, we need to check for a specific condition.
1. Symmetry with respect to the y-axis:
If a function is symmetric with respect to the y-axis, it means that if we replace x with -x in the equation of the function, it should remain unchanged. In mathematical notation, if F(x) = F(-x), then the function is symmetric with respect to the y-axis.
To check for this symmetry, we need to compare F(x) with F(-x). If they are equal, then the function is symmetric with respect to the y-axis. If they are not equal, then the function is not symmetric with respect to the y-axis.
2. Symmetry with respect to the origin:
If a function is symmetric with respect to the origin, it means that if we replace both x and y with their negations (-x and -y) in the equation of the function, it should remain unchanged. In mathematical notation, if F(x, y) = F(-x, -y), then the function is symmetric with respect to the origin.
To check for this symmetry, we need to compare F(x) with F(-x) and also check whether F(0) is equal to 0. If both conditions are satisfied, then the function is symmetric with respect to the origin. If either of the conditions is not satisfied, then the function is not symmetric with respect to the origin.
In summary, if the equation satisfies F(x) = F(-x) for symmetry with respect to the y-axis or F(x, y) = F(-x, -y) and F(0) = 0 for symmetry with respect to the origin, then the function is symmetric accordingly.
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