Dear Gabriela Guerrero,
You first question is: What are some easy ways to remember proofs?
The beauty of mathematics partially lies in the fact that there is very little to memorize. It is what sets it apart from other studies such as humanities. Memorizing proofs is counterproductive in the long run. You should rather develop your personal approaches in order to be ready to prove any proposition. Profoundly understanding the meaning of a mathematical proof will aid you in this process. A proof is a demonstration that some statement is necessarily true. A proof is a logical argument, not an empirical one. This means one must demonstrate that a proposition is true in all cases before it is considered a theorem of mathematics. Gabriela, there are many types of proofs. Which proofs are you concerned about?
Your second question is: Are there any short-cuts to graph equations?
Let me reinterpret your question, since unless you are combining equations in your calculator, using your TI-83 to graph shouldn’t need any shortcut.
Are there any short-cuts to graph equations by hand?
You already know about connecting dots or points of a function in order to reveal its graph. If you can determine that a function follows a certain pattern, or that it is symmetric about a certain axis, then you can complete a graph without placing as much dots. Such is the case of y = │x│+ C, where C is any constant. This approach, however, is vulnerable to cause an overly inexact graph that may take points away during an examination, unless you are a really talented drawer.
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