UNIT 9 LESSON 1
INTRO TO FUNCTIONS
SECONDARY II
OBJECTIVES
• Tell if a relation is a function
• Find the value of a function
FUNCTION
A function is a relation in which each element in the
domain (input) of the relation corresponds to exactly one
element in the range (output).
SHORT VERION
An 𝑥 goes to a unique 𝑦
FUNCTION - MAP
A) Does the mapping represent a function? EXPLAIN
0.71
0.73
0.74
0.76
0.86
DIAMOND KARAT
$1,990
$2,446
$2,057
$3,067
$3,329
$3,097
PRICE
FUNCTION - MAP
B) Does the mapping represent a function? EXPLAIN
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AGE
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34
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HDL CHOLESTEROL
FUNCTION
All functions are relations but not all relations are function.
A function is simply a specific type of relation.
FUNCTION - POINTS
Are the following sets of points a function? EXPLAIN
C) {(1,3), (−1,4), (0,6), (2, 8)}
D) {(−2, 6), (−1,3), (0,2), (1,3), (2, 6)}
E) {(0,3), (1,4), (4, 5), (9,5), (4, 1)}
FUNCTION - EQUATION
Are the following equations a function? EXPLAIN
F) 𝑦 = −2𝑥 + 5 G) 𝑦 = ±3𝑥
H) 𝑦 = 𝑥2 + 5𝑥 I) 𝑥 + 𝑦2 = 9
FUNCTION - GRAPH
To determine if a graph is a function we can use the Vertical Line Test.
A set of points in the 𝑥𝑦 plane represent a function if and only if every vertical line intersects the graph in at most one point.
SHORT VERSION: Vertical line can’t cross twice
FUNCTION - GRAPH
Are the following graphs a function? EXPLAIN
J) K)
FUNCTION - GRAPH
Are the following graphs a function? EXPLAIN
L) M) N)
FUNCTION - NOTATION
If 𝑓 is a function, then for each number 𝑥 in its domain
there is a corresponding value in the range 𝑦, or 𝑓(𝑥).
𝑓(𝑥) means “the value of 𝑓 at the number 𝑥.”
Because 𝑦 = 3𝑥 + 2 is a function, it can be rewritten as
𝑓 𝑥 = 3𝑥 + 2
FUNCTION - NOTATION
For a function 𝑓(𝑥)
𝑥 is called the independent variable.
𝑓(𝑥) [or 𝑦] is called the dependent variable.
FUNCTION - NOTATION
Find the value of the function 𝑓 𝑥 = 𝑥2 + 5𝑥
O) 𝑓 3 = P) 𝑓 −2 =
Q) 𝑓1
5= R) 𝑓 2𝑥 =
OBJECTIVES
• Tell if a relation is a function
• Find the value of a function
CHECK FOR UNDERSTANDING
In Class Assignment 9.1
Homework 9.1
EDPuzzle 9.1