Domain and Range

Domain- the interval of x values where the graph exists.

Range- the interval of y values where the graph exists.

Zeros, x intercept, root set = to 0, solve 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 a list of all y-values in { }.

To find Domain and Range:

1. Polynomials- x=line, x^2=parabola, x^3 = squiggly

Domain: (-infinity, infinity)

Range: odd(x, x^3)(-inf, inf) x^2; x^2:(-b/2a, inf) if graph points up or (-inf, -b/2a) if graph points down.

2. Square root y = sqrt(x+or- #) +or- a

Domain: a. set inside the root = 0 and solve

b. set up intervals

c. plug in if you et a negative x the interval

d. write answer in interval notation; use '[' by the number. ex: Range [a, inf)

3. Square root y = sqrt(#-x^2) +or- a

Domain: a. set inside = 0, solve

b. put ans in [-#, #]

Range: a.[0, sqrt(#)] if a = 0

b.[0+a, sqrt(#) + a] if a is positive

c. [0-a, sqrt(#)-a] if a is negative

4. Fraction: asymptotes

a. Factor top and bottom

2. cancel if possible and move the number connected

3. set bottom = 0 and solve for x values

4. write in interval notation stopping at numbers found in 2 and 3

5. Absolute Value: pointy parabolas, y = |x +or- #| +or- a

Domain: (-inf, inf)

Range: [0+a, inf) if pointy parabola(pp) + a is positive

[0-a, inf) if pp + a is negative