Domain, Range, and Symmetry Unit 2 – Day 1 Domain, Range, and Symmetry

Domain and Range Always use interval notation!!!! When the value is NOT a part of the function – “open” … When the value IS a part of the functions – “closed” … When there is a JUMP in the function – “OR” …

Example 1 Domain: Range:

Example 2 Domain: Range:

Example 3 Domain: Range:

Example 4 Domain: Range:

Example 5 Domain: Range:

Example 6 Domain: Range:

Finding DOMAIN Find all holes and/or vertical asymptotes Exclude holes and V.A. from domain EXs:

Common Domain Restrictions Polynomial Functions have NO domain restrictions, since they are all continuous!! Therefore, the domain is always R. Example: 𝑓 𝑥 = 𝑥 2 +3𝑥+1 Example: 𝑓 𝑥 =2𝑥−1

Common Domain Restrictions Fractions!!! Set denominator = 0 and exclude NON-solutions from the domain. Example: 𝑓 𝑥 = 2𝑥+1 (𝑥+2)(𝑥−3) Example: 𝑓 𝑥 = 2 𝑥 2 −3

Common Domain Restrictions Square Roots!!! Set radicand≥ 0 and solve for possible interval of solutions. Example: 𝑓 𝑥 = 𝑥+1 Example: 𝑓 𝑥 = 𝑥 −12

Common Domain Restrictions Square Roots in DENOMINATORS!!! Set radicand > 0 and solve for possible interval of solutions. Example: 𝑓 𝑥 = 𝑥 2 +2𝑥+3 𝑥+1

Finding RANGE Find all holes and/or horizontal asymptotes Exclude holes and H.A. from range EXs:

2 Types of Symmetry Even: symmetric across the y-axis Sketch an example: Odd: symmetric about the origin

Even Symmetry Examples: Graph: Table: Algebra:

Odd Symmetry Examples: Graph: Table: Algebra:

Neither Examples: Graph: Table: Algebra: