Question

(a) If the point \(\left( {5,3} \right)\) is on the graph of an even function, what other point must also be on the graph?

(b) If the point \(\left( {5,3} \right)\) is on the graph of an odd function, what other point must also be on the graph?

Short answer

1. The point \(\left( { - 5,3} \right)\) must also be on the graph.
2. The point \(\left( { - 5, - 3} \right)\) must also be on the graph.

Step-by-step solution

Define the graph of an even and an odd function

The graph of an even function is symmetricwith respect to the \(y\)-axis. And the graph of an odd functionis symmetric with respect to the origin.

Determine the other point that must be on the graph

(a)

The point\(\left( {5,3} \right)\)must be on the graph of the even function since the graph of an even function is symmetric with respect to the\(y\)-axis.

Therefore, the point \(\left( { - 5,3} \right)\) must also be on the graph.

Determine the other point that must be on the graph

(b)

The point\(\left( {5,3} \right)\)must be on the graph of the odd function since the graph of an odd function is symmetric with respect to the origin.

Therefore, the point \(\left( { - 5, - 3} \right)\) must also be on the graph.