1. Functions Basic Concepts Value (Image), Domain, Range, Graph

2. Examples of Real functions 1. : a. f(x) = 9 Constant function b. Power functions f(x)=x n, where n is a natural number Examples: f(x) = x The identity function f(x) = x 2 The squaring function f(x) = x 3 The cubing function The domain of each of these functions is R

3. b. Power functions f(x)=x n, where n is a negative integer number. Examples: f(x) = 1/x The inverting function f(x) = 1/x 2 Inverting the square function f(x) = 1/x 3 Inverting the cube function The domain of each of these functions is R – {0}

4. Polynomial Functions Examples: 1. f(x) = any power function 2. f(x) = 8x 9 + 6x 5 -7x 2 - x + 12 3. f(x) = 2x 3 - 1

5. Rational Functions A rational function is a function of the form p(x)/q(x), where p(x) and q(x) are polynomials Examples of rational functions are all polynomial functions and hence all power functions. The domain of a rational functions is the set of all real Numbers which are not zeroes (roots) of the polynomial in the denominator.

7. Examples I Determine domain f, and the values: f(1), f(-2), f(0) and f(4) for the given function f

8. Examples (1) Determine domain f, and the values: f(1), f(-2), f(0) and f(4) for the given function f

16. Graph of f(x) = 2x + 4

18. Graph of f(x) = x + 3

24. Case-Defined Function (Piecewise Defined Function)

27. How to graph this function?