Determine whether the graph of each function is symmetric with respect to the origin.

F(X)=-12/x

f(x) = 12/x

f(-x) = -12/-x = 12/x

so f(x) = - f(-x)

yes, there is symmetry about the origin.

To determine whether the graph of the function f(x) = -12/x is symmetric with respect to the origin, we need to check if the function satisfies the condition f(-x) = -f(x).

1. Substitute -x for x in the function: f(-x) = -12/(-x).
2. Simplify the expression: f(-x) = 12/x.
3. Next, substitute x back into the original function: f(x) = -12/x.
4. Compare f(-x) = 12/x to -f(x) = -(-12/x) = 12/x.

Since f(-x) = 12/x is equal to -f(x) = 12/x, the function f(x) = -12/x is symmetric with respect to the origin.

Therefore, the graph of the function is symmetric with respect to the origin.

To determine whether the graph of a function is symmetric with respect to the origin, we need to check if the function satisfies the condition f(-x) = -f(x) for any value of x.

Given the function f(x) = -12/x, we'll substitute -x into the function and check if it equals -f(x):

f(-x) = -12/(-x) = 12/x

Now, we'll check if -f(x) is equal to f(-x):

-f(x) = -(-12/x) = 12/x

Since f(-x) = -f(x), we can conclude that the graph of the function f(x) = -12/x is symmetric with respect to the origin.