Chapter 4

Domain and Range:-Domain- the interval of x values where the graph exist
-Range- the interval of y values whre the graph exist
-Zeros, x-intercept, root - set = 0, slove for x
-To be a function the graph must pass the vertical line test
-If given points the domain is the list of all x-values and range is of all y-values in { }

To find Domain and Range:
-Polynomials: domain and always (negative infinity, positive infinity)
-Square root: 1. Set inside root equal to 0 and solve
                      2. Set up intervals
                      3. Plug in if you get a negative x interval
                      4. Write answer in interval notation- use brackets by the number Range: [ a, infinity)
-Square root: Domain: 1. Set inside equal to 0 and solve
                                     2. Put answer in [-   ]
                      Range: [0, square root of number] if a=0
                                  [0 plus or minus a, square root of a number + a] if a is positive
                                  [0 minus a, square root of a number minus a] if a is neagtive
-Fraction: Domain: 1. Factor top and bottom
                                2. Cancell if possible and marke # if cancelled
                                3. Set bottom equal to 0 and slove for x value
                                4. Write in interval notation stopping at numbers found in 2 and 3
-Absolute Value: Domina: (- infinity, positive infinity)
                             Range: [0 + a, infinity) if v is ponted up and a is positive
                                         [0 - a, infinity) if v is pointed up and a is negative
                                         (- infinity, 0 - a] if v is ponted down and a is negative
                                         (- infinty, 0 +a] uf v is pointed down and a is positive


Example 1: Find the Domain and Range of the following: f(x) = 5x^3 + 4x^2 + 3x - 6

 Domain: (- infinity, infinity)
 Range: (- infinity, infinity)

Funtion? Yes


--Daniellee