4-1

4-1
In Advanced Math we’re stepping out of trig for a while and going back to Chapter 4. Section 4-1 is about finding domain and range. Domain is from left to right and range is from bottom to top. There are a few guidelines to follow:

1. Polynomial (an equation with no variables in the denominator)
Domain: ALWAYS (-infinity, infinity)
Range: (-infinity, infinity) if exponent is odd

2. Square roots
Domain: A). Set inside =0 and solve for x.
B). Set up a number line.
C). Plug in numbers, use the non-neg intervals.
Range: (vertical shift, infinity)
** If square root #-x^2 then range is [0, +/- square root #)

3. Fractions
Domain: A). Set bottom =0 and solve for x.
B). Set up intervals.
Range: A). Take limit as x – infinity.
B). Set up intervals.
** Always use () with fractions.

4. Absolute Value
Domain: (-infinity, infinity)
Range: [shift, infinity) if + and (-infinity, shift] if –.

EX 1: Find domain and range: 2x^3+3x^2-6x
A). This is a polynomial, so the domain is automatically (-infinity, infinity).
C). The exponent of 2x is 3, which is odd, so we know that the range will be (-infinity, infinity).

EX 2: Find the domain and range: 2/x-3.
A). This is a fraction so we know we’re going to have to set the bottom =0 to find domain.
B). x-3=0, so x=3
C). The domain will be (-infinity, 3)u(3, infinity)
D). Now to find the range, find the limit. This is going back to Chapter 13.
E). According to the limit rules, it’s 0.
F). So, the range is (-infinity, 0)u(0, infinity)