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

2. 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” …

3. Example 1
Domain:
Range:

4. Example 2
Domain:
Range:

5. Example 3
Domain:
Range:

6. Example 4
Domain:
Range:

7. Example 5
Domain:
Range:

8. Example 6
Domain:
Range:

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

10. 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

11. 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

12. 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

13. 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

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

15. 2 Types of Symmetry Even: symmetric across the y-axis
Sketch an example:
Odd: symmetric about the origin

16. Even Symmetry
Examples: Graph: Table: Algebra:

17. Odd Symmetry
Examples: Graph: Table: Algebra:

18. Neither
Examples: Graph: Table: Algebra: