Question

1. determine whether the following graphs represent functions that are even, odd, or neither.

Explanation:

Step1: Recall Function Symmetry Rules

• Even Function: Graph is symmetric about the \( y \)-axis. For all \( x \), \( f(-x)=f(x) \).
• Odd Function: Graph is symmetric about the origin. For all \( x \), \( f(-x)= -f(x) \) (symmetric over \( 180^\circ \) rotation about origin).
• Neither: Does not satisfy either symmetry.

Step2: Analyze Graph A

• Check symmetry. The graph does not mirror over \( y \)-axis (left and right sides differ) and does not have origin symmetry (rotating \( 180^\circ \) about origin does not map to itself). So Graph A: Neither.

Step3: Analyze Graph B

• Check symmetry. The graph is symmetric about the origin (rotating \( 180^\circ \) about origin maps the graph to itself) but not about \( y \)-axis. So Graph B: Odd.

Step4: Analyze Graph C

• Check symmetry. The graph is symmetric about the \( y \)-axis (left side mirrors right side). So Graph C: Even.

Answer:

• Graph A: Neither
• Graph B: Odd
• Graph C: Even