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Big Ideas:
Given two functions, f(x) and g(x), the x-coordinates of the points where two equations intersect are the solutions of the equation f(x)=g(x).
In this task, students graph a system of equations including a rational function that relates the number of people attending an end of the year trip to the cost per person of the trip, as well as a fixed linear function relating number of people attending the trip to total fixed cost. Students find the point of intersection of the two graphs and interpret this point of intersection in the context of the problem. This task differs from Task 8 because the numerator of the rational function is not constant, and the graph of the total cost function is an oblique line.
Vocabulary: graph, plot, point, system of equations, function, rational, linear, intersection, solution
Special Materials:
Graph paper