identify whether the graph of the function ( f(x) ) shown below is even, odd, or neither.
identify whether the graph of the function ( f(x) ) shown below is even, odd, or neither.
Answer
Explanation:
Step1: Recall the definition of an odd function
An odd function satisfies ( f(-x)=-f(x) ). Its graph is symmetric about the origin.
Step2: Recall the definition of an even function
An even function satisfies ( f(-x) = f(x) ). Its graph is symmetric about the ( y )-axis.
Step3: Analyze the graph
If we rotate the graph of the function ( f(x) ) ( 180^{\circ} ) about the origin, the graph does not coincide with itself. Also, if we reflect the graph about the ( y )-axis, the graph does not coincide with itself.
Answer:
Neither.