Question

79-80 the graph of a function defined for \(x \ge 0\) is given. Complete the graph for \(x < 0\) to make (a) an even function and (b) an odd function.

79.

Short answer

The graph of \(f\) for an even function and an odd function is obtained.

Step-by-step solution

Define the graph of an even and an odd function

The graph of an even functionissymmetric with respect to the\(y\)-axis. The graph of anodd functionissymmetricwith respect to the origin.

Complete the graph for \(x < 0\) to make (a) an even function

a)

The graph of an even function is symmetric around the \(y\)-axis.

Complete the graph by reflecting the given portion of the graph of \(f\) around the \(y\)-axis.

Complete the graph for \(x < 0\) to make (b) an odd function

b)

The function \(f\) is odd if it satisfies \(f\left( { - x} \right) = - f\left( x \right)\) for all real numbers \(x\).

The graph of an odd function is symmetric around the origin.

Complete the graph by rotating the given portion of the graph of \(f\) through \(180^\circ \)about the origin.