1. You identified domains and ranges for given situations.
Analyze relations and functions.
Use equations of relations and functions.
Then/Now

2. 2-1 Relations and Functions
Analyze and use relations and functions
Discrete vs Continuous Functions

3. Concept 1

4. The relation is {(1, 2), (3, 3), (0, –2), (–4, –2), (–3, 1)}.
Domain and Range
State the domain and range of the relation. Then determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.
The relation is {(1, 2), (3, 3), (0, –2), (–4, –2), (–3, 1)}.
Answer: The domain is {–4, –3, 0, 1, 3}. The range is {–2, 1, 2, 3}.
Each member of the domain is paired with one unique member of the range, so this relation is a function. It is onto, but not one-to-one.
Example 1

5. Concept 2

6. State the domain and range of each relation
State the domain and range of each relation. Determine whether it is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.

7. Discrete relation: A set of individual points where it doesn’t make sense to connect the points. (Domain is whole number, for example, graphing the number of candy bars sold each day from the candy machine) Continuous relation: Domain has an infinite number of elements and the graph could be a line or smooth curve.

10. Independent variable: the variable (usually x) that determines the domain.
Dependent variable: the other variable (usually y) that is determined by what you put in for x.

11. Function notation: Commonly used f(x), g(x), h(x), j(x)
Function notation: Commonly used f(x), g(x), h(x), j(x). Tells you what the x in equation is being replaced by. Function notation could be thought of as y.

12. B. Given f(x) = x2 + 5, find f(3a).
A. 3a2 + 5
B. a2 + 8
C. 6a2 + 5
D. 9a2 + 5
Example 4B