ANSWER and EXPLANATION
We want to answer the questions about the qualities of the given graph.
The degree of a graph can be easily determined by adding 1 to the number of turning points that a graph has. The given graph has 5 turning points, which means that it has a degree of 6. Hence, its degree is even.
The leading coefficient of a graph can be determined by checking how the graph opens up. If the graph opens upward, it has a positive leading coefficient while if it opens downward, it has a negative leading coefficient. Since the given graph opens upward, it has a positive leading coefficient.
The distinct zeros of the graph of a function are the points where the graph touches the x-axis. The given graph touches the x-axis at 5 different points, so it has 5 distinct real zeros.
The relative extreme values of a graph are the peaks and valleys of the graph. The graph has 5 peaks and valleys, hence, it has 5 relative extreme values.
Hence, the degree of f(x) is even and the leading coefficient is positive. There are 5 distinct real zeros and 5 relative extreme values.