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

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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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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