Question

Graphs of\({\bf{f}}\)and\({\bf{g}}\)are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.

Short answer

The graph of function f is neither odd nor even and the graph of function g is an even function.

Step-by-step solution

Identification of graph f

The graph of odd functions is symmetric about the origin and the graph of even functions is symmetric about the y axis. The graph of function f is neither symmetric about the line \(y = x\) passing through origin in opposite quadrants nor it is symmetric about the y axis, so the graph of function f is neither odd nor even.

Identification of graph g

The graph of function g is symmetric about the y axis in opposite quadrants. The half portion of graph g is lying in the third quadrant left to the y-axis and the other half is lying in the fourth quadrant right to the y-axis, so the graph of function g shows that function g is an even function.