Helen's Blog

Finding Domain and Range:

1) Polynomial- an equation with no variables in the denominator.

domain: always (- infinity, infinity)
range: (-infinity, infinity) if the largest exponent is odd

2) Square Roots

domain: a) set inside = 0 and solve for x
b) set up a number line
c) plug in the numbers, use the non-negative interval

range: [vertical shift, infinity)

3) Fractions

domain: a) set bottom = 0 solve for x
b) set up intervals

range: a) take limit as x-> infinity
b) set up intervals

4) Absolute Value

domain: ( -infinity, infinity)

range: [ shift, infinity) or ( -infinity, shift]


Examples:

1) 3x^3 + 4x^2-7x

domain: ( - infinity, infinity)
range: ( - inifinity, infinity)

2) x+1/ x^2+5x+6

D: x^2+5x+6
(x+3)(x+2)

D: (- infinity, -3)u(-3,-2)u(-2, infinity)

R: ( -infinity,0)u(0,infinity)