In an alternative math world, 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 * 5 = 10. However, ab is still used as short for a * b, and a2 means a * a. For example, 52 = 10. In this world, what will the graph of x2 + 2x + 1 look like?
I will use the notation alt() and norm() to indicate which version of math the expression within parentheses should be used.
So the equation alt(x^2 + 2x + 1) means
alt(A + B + C) where A,B,C are
A is norm(x+x)
B is norm(x+2)
C is 1
and alt(A + B + C) means norm(max(A,B,C))
max(2x, 2+x, 1)
A=B at x = 2
A=C at x = 1/2
B=C at x = -1
if x > 2: 2x
if 1/2 < x < 2: x+2
if -1 < x < 1/2: x+2
if x < -1: 1
or the function equals:
2x, if x >= 2
x+2, if -1 < x < 2
1, if x <= -1
https://www.desmos.com/calculator/qq6tf2cg1z
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Posted by Larry
on 2025-01-16 14:50:42 |
solution