Domain and Range

This is Chapter 4: Section 1.

This you should know:

• Domain-the interval of x values where the graph exists.
• Range-the interval of y values where the graph exists.
• Zeroes-x intercept, root-set equal to zero, and solve for x.
• A graph must pass the vertical line test in order to be a function.
• If you are given points, the domain will be the list of all x-values and range will be the list of all y values. It will be in { }.

How to find domain and range for polynomials and absolute values:

• Polynomials: Domain will always be (-infinity, infinity). Range- (-infinity, infinity), if it is x^2-(-b/2a, infinity) or (-infinity, -b/2a).
• Absolute values: Domain-(-infinity, infinity). Range-[0+a, infinity) or (-infinity, 0+a] if a is positive, [0-a, infinity) or (-infinity, 0-a] if a is negative.

Example 1: Find the domain and range of the following: f(x)=7x^3+4x^2+x-9

• Domain=(-infinity, infinity)
• Range=(-infinity, infinity)

Example 2: Find the domain and range of the following: f(x)=-5x^2+8x-10

• Domain=(-infinity, infinity)
• Range=(-infinity, -8/2(-5))=(-infinity, -8/-10)=(-infinity, 4/5)

Example 3: Find the domain and range of the following: y=|x-6|+2

• Domain= (-infinity, infinity)
• Range=[2, infinity)

Amber :)