Domain and Range of Polynomials and Fractions

*Domain-the interval of x vallues where the graph exists.
*Rage-the interval of y values where the graph exists.

*For zeros x-intercept, root -set = o. Solve for x.
*To be a function the graph must pass the vertical line test. For this you draw lines up and down to see if part of the graph crosses the line twice. If if crosses any line more than once it is not a function.
*If given points, the domain is the list of all x values, while range is a list of all y values in a set of points indicated.

1.Polynomials
Domain: 00 or -00 always
Range: odd (-oo or 00). X^2 always (-b/2a, 00) or (-oo, -b/2a)

2.Fractions
Domain: -factor top and bottom
-cancel if possible (mark #)
-set bottom = 0, then solve the x value
-write in inteval notation stopping at #s foudn in { }
Range: is none

EX1. Find the domain and range of 3+2x^5
Domain = -oo, oo
Range= -oo, 00

EX2. Is the following a function? (2,-3) (4,-2) (2,2) , (3, -2)
No! when drawn out in a graph it does not pass the vertical line test.

EX3. (x-2) (x-3)/(x-6) (x-3) Find domain and range
-cancel the pay attenction only to top numbers
Domain= (-oo, 3) u (3,6) u (6, 00)
Range= none