Question

A function has a domain\(\left( {{\bf{ - 5,5}}} \right)\)and a portion of its graph is shown.

(1) Complete the graph of if it is known that is even.

(2) Complete the graph of if it is known that is odd.

Short answer

(1) The complete graph of the even function is shown infigure (1).

(2) The complete graph of the even function is shown in figure (2).

Step-by-step solution

Determination of another half of the graph for even function

(1)

The graph of the even function is always symmetric about the y axis in opposite quadrants so the other half of the given graph will be in the second quadrant. The complete graph of the function is given below in figure (1). Therefore, the complete graph of the even function is shown in figure (1).

Figure (1)

Determination of another half of the graph for odd function

(2)

The graph of an odd function is always symmetric about lines \(y = x\) or \(y = - x\) in opposite quadrants so the other half of the given graph will be in the third quadrant. The complete graph of the function is given below in figure (2). Therefore, the complete graph of the even function is shown in figure (2).

Figure (2)