the graph of a function is given. decide whether it is even, odd, or neither. 8) 9) 10)

the graph of a function is given. decide whether it is even, odd, or neither. 8) 9) 10)

the graph of a function is given. decide whether it is even, odd, or neither. 8) 9) 10)

Answer

Explanation:

Step1: Recall function - parity rules

An even - function has a graph symmetric about the y - axis ($f(x)=f( - x)$). An odd - function has a graph symmetric about the origin ($f(-x)=-f(x)$).

Step2: Analyze graph 8

The graph of the function in 8 is symmetric about the y - axis. For every point $(x,y)$ on the graph, the point $(-x,y)$ is also on the graph. So it is an even function.

Step3: Analyze graph 9

The graph of the function in 9 is symmetric about the origin. For every point $(x,y)$ on the graph, the point $(-x, - y)$ is on the graph. So it is an odd function.

Step4: Analyze graph 10

The graph of the function in 10 is neither symmetric about the y - axis nor about the origin. So it is neither an even nor an odd function.

Answer:

  1. Even
  2. Odd
  3. Neither