Answer:
The degree of f(x) is even, and the leading coefficient is negative. There are 3 real zeros, and 1 relative minimum values.
Step-by-step explanation:
We have the graph of f(x).
First, since both end behaviors are the same, our function must be an even-degree.
Second, since both end behaviors are going towards negative infinity, this means that the leading coefficient of our function must be negative.
The real zeros are whenever the graph touches or crosses the x-axis. We can see that this happens three times. I've circled them in blue in the image below.
Finally, relative minimum values are the lowest points in a graph, and then happen between a decreasing and then an increasing curve.
From, the graph, we only have one relative minimum value. This is circled in black in the image below.
Note that the arrows whether the curve is decreasing or increasing. We can see that the curve to the left of the minimum is <em>decreasing</em>, while the curve to the right of the minimum is <em>increasing</em>.
So, our solution is:
The degree of f(x) is even, and the leading coefficient is negative. There are 3 real zeros, and 1 relative minimum values.
And we're done!
