Q57. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The graph represents an odd-degree function and has three real zeroes.

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 in opposite direction. So, the graph represents an odd-degree function.

As the graph crosses x-axis three times, the function has three real zeroes.

Step 3. Conclusion .

Hence the graph represents an odd-degree function and has three real zeroes.