Question

Determine whether each graph represents an odd-degree function or an even-degree function. Then state how many real zeroes each function has.

Short answer

The graph represents an even-degree function and has two real zeroes.

Step-by-step solution

Step 1. Given Information.

It is to be determined whether the given graph represents an odd-degree function or an even-degree function.

Then the number of real zeroes of each function is to be determined.

Step 2. Explanation.

The end behaviour of a graph is given as:

When both ends of the graph open in the same direction, then the graph is even-degree function.

When both ends of the graph open in opposite direction, then the graph is odd-degree function.

From the given graph, both the ends open upwards i.e., same direction. So, the graph represents an even-degree function.

As the graph crosses x-axis twice, the function has two real zeroes.

Step 3. Conclusion.

Hence the graph represents an even-degree function and has two real zeroes.