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Advanced Math / Nonlinear functions Difficulty: Medium

A competitive diver dives from a platform into the water. The graph shown gives the height above the water $y$ , in meters, of the diver $x$ seconds after diving from the platform. What is the best interpretation of the x-intercept of the graph?

The diver reaches a maximum height above the water at $1.6$ seconds.

The diver hits the water at $1.6$ seconds.

The diver reaches a maximum height above the water at $0.2$ seconds.

The diver hits the water at $0.2$ seconds.

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Explanation

Choice B is correct. It’s given that the graph shows the height above the water $y$ , in meters, of a diver $x$ seconds after diving from a platform. The x-intercept of a graph is the point at which the graph intersects the x-axis, or when the value of $y$ is $0$ . The graph shown intersects the x-axis between $x equals 1$ and $x equals 2$ . In other words, the diver is $0$ meters above the water, or hits the water, between $1$ and $2$ seconds after diving from the platform. Of the given choices, only choice B includes an interpretation where the diver hits the water between $1$ and $2$ seconds. Therefore, the best interpretation of the x-intercept of the graph is the diver hits the water at $1.6$ seconds.

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect. This is the best interpretation of the maximum value, not the x-intercept, of the graph.

Choice D is incorrect and may result from conceptual errors.