Question

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

Short answer

The graph of function f is an odd function and the graph of function g is an even function.

Step-by-step solution

Identification of graph f

The graphs of odd functions are symmetric about the origin and the graph of even functions is symmetric about the y-axis.The graph of function f is symmetric about the line \(y = x\) passing through origin in opposite quadrants. The half portion of graph f is lying in the second quadrant above line y=x and the other half is lying in the fourth quadrant below the line y=x, so the graph of function f shows that function f is an odd function.

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 second quadrant left to the y-axis and the other half is lying in the first quadrant right to the y-axis, so the graph of function g shows that function g is an even function.