Topics:
• Some problems from the textbook on functions which are defined by tables: Exercise 2.5
• More on functions: various ways of defining functions, and using function notation. (Session 2, Examples 2.16, 2.19, 2.20)
Please note that the purpose of these examples is to get you familiar with the concept of a function and the vocabulary and notation that is used.
• Functions defined by formulas: Session 3
• Domains of functions defined by formulas
Here are some notes on the examples I discussed in class:
MAT1375-FunctionsByFormulas-slideshow
In general, the domain of a function is the largest possible set of the real numbers for which the formula works. Polynomial functions are good for all real number inputs, so they have domain the set of all real numbers.
For a square root function, the radicand must be greater than or equal to 0. This gives an inequality that you solve to find the domain.
For a rational function, we need the denominator to be non-zero. This again gives an inequality (with a $\neq$ sign) that you solve to find the domain.
• A difference quotient computation (Example 3.2(h-k))
It is strongly recommended that you compute difference quotients step by step as is done in this example.
