Final answer:
The student's question is related to correcting a mathematical expression or equation, which may involve exponential functions, trigonometry, and proper bracket pairing for clarity in function definition.
Step-by-step explanation:
The student appears to be looking for assistance with correcting an equation or expression related to mathematics. Without the complete context, it's challenging to provide a comprehensive correction, but based on the fragments provided, it seems that there may be a need to clarify either the proper formulation of an equation or the correct way to graph or interpret the graph of given functions. Concerning the notations presented such as 'y = {x^3 + 2x}{5 + cos(x)}' and 'y =(x-2)^3', we should ensure proper use of parentheses and clarity in function definition.
When graphing functions like 'y=e^x', 'y=e^{-x}', and 'y = -e^x', it is important to understand how exponential growth and decay are represented on a two-dimensional plane. The student should note how the base of the exponential function affects its growth rate, direction, and reflection across the x- or y-axis. As for interpreting square roots and powers, understanding that, for example, x^2 is equivalent to the square root of x squared, or the principle of superposition as '5^1 · 5^1 = 5', are foundational concepts.
The student may also benefit from understanding the role of trigonometric functions and their properties, such as the average value of cosine squared or sine squared over a complete cycle, or conditions for specific values like when the argument of the cosine is an integral multiple of π/2.