Question

for each of the following graphs, identify whether it is the graph of an even function, odd function, or neither.

even

odd

neither

Explanation:

Analyze symmetry about the y-axis

$$ f(-x) eq f(x) \quad \text{since } f(-1) = 1 \text{ but } f(1) = -1 $$

Analyze symmetry about the origin

$$ f(-x) = -f(x) \quad \text{since } f(-1) = 1 = -f(1) \text{ and } f(-2) = -3 = -f(2) $$

Determine function parity

$$ \text{The graph is symmetric with respect to the origin, which defines an odd function.} $$

Answer:

• Even
• Odd (Correct answer)
• Neither