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Advanced Math / Nonlinear functions Difficulty: Easy
The figure presents the graph of a curve. The x axis is labeled “Elevation, in meters,” and the numbers 0 through 3,000, in increments of 500, are indicated. There are vertical gridlines drawn in between. The y axis is labeled “Measure of plant diversity,” and the numbers 0 through 14,000, in increments of 2,000, are indicated. The curve begins on the vertical axis at a point slightly above 10,000. The curve moves upward and to the right until it reaches its maximum at the point with coordinates 1,250 comma 13,000. Then the curve moves downward and to the right until it ends at 3,500 on the horizontal axis.

The quadratic function graphed above models a particular measure of plant diversity as a function of the elevation in a region of Switzerland. According to the model, which of the following is closest to the elevation, in meters, at which plant diversity is greatest?

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Explanation

Choice C is correct. Each point with coordinates x comma y on the graph represents the elevation x, in meters, and the corresponding measure of plant diversity y in a region of Switzerland. Therefore, the point on the graph with the greatest y-coordinate represents the location that has the greatest measure of plant diversity in the region. The greatest y-coordinate of any point on the graph is approximately 13,500. The x-coordinate of that point is approximately 1,250. Therefore, the closest elevation at which the plant diversity is the greatest is 1,250 meters.

Choice A is incorrect. This value is closest to the greatest y-coordinate of any point on the graph and therefore represents the greatest measure of plant diversity, not the elevation where the greatest measure of plant diversity occurs. Choice B is incorrect. At an elevation of 3,000 meters the measure of plant diversity is approximately 4,000. Because there are points on the graph with greater y-coordinates, 4,000 can’t be the greatest measure of plant diversity, and 3,000 meters isn’t the elevation at which the greatest measure of plant diversity occurs. Choice D is incorrect. At an elevation of 250 meters, the measure of plant diversity is approximately 11,000. Because there are points on the graph with greater y-coordinates, 11,000 can’t be the greatest measure of plant diversity and 250 meters isn’t the elevation at which the greatest measure of plant diversity occurs.