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What are the three views of a function?
rule, table of values and graph
What is a rule that assigns a unique y value to every x value?
It is a function from the set of x-values to the set of y-values.
Use Trapezoidal rule to evaluate the approximate values of definite integrals?
Yes.
How can you tell something is a function when you are given values of the function?
If you know some values, then you at least have a function of some sort, but you don't know what other values might be. To be a useful function you must be aware that a rule exists to calculate its value for any situation, and preferably know what the rule (equation or whatever) is.
How do you create a table of values for each rule with at least four values for x?
For each rule draw a table with 5 rows and 2 columns. At the top of each table write a caption denoting which rule applies to that particular table. In the top row of each table write the letter "X" in the first column and the letter "Y" in the second column. Now for each table in the first column in rows 2,3,4, and 5 write the values of X that apply to the experiment. Now apply the rule for each value of X for a particular table (particular rule) and write the value of Y (obtained by observation or calculation) in the corresponding column
