1. 1-7 Functions Objectives: Determine whether a relation is a function.
Find function values.
F.IF.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
1-7 Functions

2. Function: Relationship between input and output
Function: Relationship between input and output. There is exactly one output for each input.

3. Example 1: Determine whether each relation is a function. Explain.

4. Graph that consists of points that are not connected is a discrete function.
A function graphed with a smooth curve is a continuous function.

5. Example 2: Tell whether the graph would be continuous or discrete.
a. A truck driver enters a street, drives at a constant speed, stops at a light, then continues. CONTINUOUS or DISCRETE? b. A candy store started with 10 pieces of candy and makes 20 more each day.
Example 2: Tell whether the graph would be continuous or discrete.

6. Example 3: Function or not?
Vertical Line Test:
Helps see if a graph represents a function.
If vertical a line intersects the graph more than once, then the graph is not a function.

7. Representations of Functions
Representations of a Function
Table
Mapping
Equation
Graph
𝑓 𝑥 = 1 2 𝑥 2 −1

8. Function Notation 𝑓 𝑥 =3𝑥−8 instead of 𝑦=3𝑥−8
𝑥 represents the elements of the domain and 𝑓 𝑥 represents the elements of the range.
Example 4: For 𝑓 𝑥 =−4𝑥+7, find each value.
a) 𝑓(2) b) 𝑓(−3)

9. 1. What is the name of the friendly skunk in Walt Disney‘s Bambi?
FLOWER
2. What popular sport was known in ancient Germany as Heidenwerfen?
BOWLING
Triva…

10. Example 5: Find each value for 𝑓 𝑥 =2 𝑥 3
a) 𝑓(4) b) 3 𝑓 𝑥 +2

11. Example 5: Find each value for 𝑓 𝑥 =2 𝑥 3
a) 𝑓(−5) d) f −3 −f(1)

12. Pages 52-53: 20-25, 27, 33 – 43 odd
Homework