Question

the graph of a function is given. decide whether it is even, odd, or neither.

Explanation:

Define even and odd functions

Using the Even and Odd Functions knowledge point, we recall their graphical symmetries:

• An even function is symmetric with respect to the \(y\)-axis.
• An odd function is symmetric with respect to the origin.

Analyze the given graph

Using the Graph Symmetry knowledge point, we inspect the graph:

• The graph starts at the point \((-3, 0)\) and curves upward to the right, passing through \((0, 2)\).
• There is no corresponding curve on the left side of the \(y\)-axis for \(x < -3\).
• Reflecting the graph across the \(y\)-axis or the origin does not yield the same graph.

Determine the symmetry type

Since the graph is not symmetric about the \(y\)-axis or the origin, the function is neither even nor odd.

Answer:

neither