y= 1
______
x^2+9
What type of symmetry?
did you mean?
y = 1/(x^2 + 9)
since it doesn't matter if you use +x or -x,
we have symmetry about the y-axis
If you meant y = 1/(x^2 + 9), then Replace x with −x and y with −y to check if there is x−axis,y−axis, or origin symmetry.
So,Not symmetric to the x-axis,
Not symmetric to the y-axis, and
Not symmetric to the origin.
Hoped it helped!
Observe the symmetry about the y-axis
http://www.wolframalpha.com/input/?i=y+%3D+1%2F(x%5E2+%2B+9)
To determine the type of symmetry of the function, you need to analyze its equation. The given equation is y = 1 / (x^2 + 9).
To find the symmetry of this function, you can use the concept of even and odd functions.
1. Even Function: A function f(x) is even if it remains unchanged when x is replaced by -x. In other words, f(x) = f(-x).
2. Odd Function: A function f(x) is odd if it changes sign when x is replaced by -x. In other words, f(x) = -f(-x).
Let's check this for the given function:
Substitute -x for x in the equation:
y(-x) = 1 / ((-x)^2 + 9)
= 1 / (x^2 + 9)
As you can see, y(-x) is equal to y(x). Therefore, the function y = 1 / (x^2 + 9) is an even function.
Hence, the symmetry of the given function is "even symmetry."