Problem 9 – Alternative Math
In an alternative math world suppose that a+b means the maximum of a and b, while a*b means the sum of a and b. For example, 2 + 3 = 3 and 5^2 = 10. In this world, which of the graphs below represents f(x) = x^2 + 2x + 1? If you choose (E) please provide a sketch of the correct graph.
All problem of the week submissions are due by 5:00 PM, Thursday the following week. Please send submissions to mathpotw@acu.edu.
There was only one correct submission from Wyatt Witemeyer.
Solution:
The answer is C. Observe that max((x + x), (2+x), 1) is what we have to find to plot the solution. When -infinity < x < -1, then max = 1. When -1 < x < 2, then max = 2 + x. When 2 < x < infinity, then max = x+x>. This means we plot the piecewise function f(x) = { 1, [-infinity, -1], x+2, [-1,2], 2x, [2,infinity]} which is answer choice (C).
