Question

Not all operators are commutative, namely, a*b = b*a.

Consider functions under the operators addition, subtraction, multiplication, division, and composition.

Pick two of the functions and use a grapher (like Desmos) to graph the functions under the operators. If the functions are commutative under the operator, the graphs should be identical (overlap everywhere) when you change the order in which the functions are entered with the operator. Determine which operators seem to the commutative and which operators seem not to be commutative using graphs as evidence. Explain what you learn.

Some functions you might use are below.

F(x)  = 2x + 1

G(x) = x^2 +2x +1

H(x) = sin(x)

I(x) = e^x

J(x) = log(x)

K(x) = 1/x

Answer 1