Question

Is f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
an even or an odd​ function? What symmetry does its graph​ exhibit?
Question content area bottom
Part 1
Is f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
an even or an odd​ function?
A.
odd
B.
even
Part 2
What symmetry does its graph​ exhibit? Select all that apply.
The graph of a function is symmetric with respect to the origin.
The graph of a function is symmetric with respect to the​ y-axis.
The graph of a function is symmetric with respect to the​ x-axis.

Answer 1

Part 1: A. odd.

Reason: f(-x) = 1/(-x) = -1/x = -f(x), and the domain is symmetric (all nonzero x), so f is odd.

Part 2: The graph is symmetric with respect to the origin only. (Not symmetric about the y-axis or x-axis.)