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Advanced Math / Nonlinear functions Difficulty: Easy

During the first part of an experiment, a ball was launched from a $7$ -foot-tall platform. The graph shows the height $y$ , in feet, of the ball $x$ seconds after it was launched during the first part of the experiment.

During the second part of the experiment, the ball was launched the same way, but from a platform that is $2$ feet shorter than the first platform. Which of the following graphs could represent the height $y$ , in feet, of the ball $x$ seconds after it was launched during the second part of the experiment?

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Explanation

Choice B is correct. It's given that $y$ represents the height, in feet, of the ball $x$ seconds after it was launched. It's also given that during the first part of an experiment, a ball was launched from a $7$ -foot-tall platform. Therefore, the y-coordinate of the y-intercept of the given graph, $7$ , represents the platform height, in feet. During the second part of the experiment, the platform the ball was launched from was $2$ feet shorter than the platform in the first part of the experiment. It follows that the height of the platform in the second part of the experiment was $7 minus 2$ feet, or $5$ feet. Therefore, the y-coordinate of the y-intercept of the graph representing the second part of the experiment must be $5$ . Only choice B satisfies this condition.

Choice A is incorrect. This could represent the graph if the ball were launched from a platform that was about $3$ feet shorter rather than $2$ feet shorter.

Choice C is incorrect. This could represent the graph if the ball were launched from a platform that was $2$ feet taller rather than $2$ feet shorter.

Choice D is incorrect. This could represent the graph if the ball were launched from a platform that was twice as tall rather than $2$ feet shorter.