Consider the graph of f(x) as shown.

Graph of f of x. The curve approaches infinity as x approaches negative infinity, then passes through the point (-3.45, 0), turns at about (-3.05, -2.03), passes through (-2.51, 0), then turns again at (-1.39, 4.62), passes through and turns at (-0.06, 0.97), then passes through (0,1) and continues up towards infinity as x approaches infinity.

The graph of f(x) shows _[blank 1]_ local maxima or minima and _[blank 2]_ inflection points, so the degree of f(x) is most likely _[blank 3]_.

im lost please help

well, geez. It says "turns" 3 times. How many max/minima is that?

It's concave up, then down, then up again, so two inflections.

It is of even degree, since it goes up on both ends.

You can see that if it were shifted down a bit, it would have four roots, right?

To determine the number of local maxima or minima and inflection points, we need to analyze the behavior of the graph of f(x) at different points.

1. Local maxima or minima: A local maximum is a point on the graph where the function reaches the highest value in a localized interval, and a local minimum is a point where the function reaches the lowest value in a localized interval. These points can occur where the slope of the graph changes from positive to negative or vice versa.

2. Inflection points: An inflection point is a point on the graph where the concavity changes from concave up to concave down or vice versa. At an inflection point, the second derivative of the function changes sign.

Now, to determine the number of local maxima or minima and inflection points in the given graph, we need to visually analyze it based on the provided information.

From the description of the graph, we can identify that there are two points where the curve changes direction: at about (-3.05, -2.03) and (-1.39, 4.62). These points can serve as potential candidates for local maxima or minima.

Additionally, there is one point of inflection mentioned at (-0.06, 0.97).

Since the graph does not mention any other turns or points where the behavior changes, we can conclude that there are no additional local maxima or minima and inflection points in the given information.

Therefore, the number of local maxima or minima is 2, the number of inflection points is 1, and the degree of f(x) is not provided or determinable from the given information.