Wednesday, October 16th

Please complete the warm up

Blast From the Past1. What is the constant in the expression

2. The product of 8 and the sum of a number and 4 is greater than 10.

Unit 3: FunctionsLinear vs.

Exponential

What is a Function? It’s like a machine! You INPUT a

number to get an OUTPUTInput: The value substituted for

xOutput: The value generated to

get y

y = 10x + 5Output Input

Let’s think About it……

Y = 3x

Input

Out put

Input: 5 Output:____Input: -2Output:___Input: 6 Output:____

An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver’s fee. Write ordered pairs for

the engraver’s fee when there are 5, 10, 15, and 20 words engraved.

Let y represent the engraver’s fee and x represent the number of words engraved.

Engraver’s fee is $10 plus $2 for each word

y = 10 + 2 · x

y = 10 + 2x

Real World Application

Number ofWordsEngraved

Rule Charges Ordered Pair

x (input) y = 10 + 2x y (output) (x, y)y = 10 + 2(5)5 20 (5, 20)

y = 10 + 2(10)10 30 (10, 30)

y = 10 + 2(15)15 40 (15, 40)

y = 10 + 2(20)20 50 (20, 50)

Organizing it All

RelationAny set of input that has an output

Input and output values are ordered

FunctionA relation is where EACH input

has exactly ONE outputEach element from the domain is

paired with one and only one element from the range

Different input values can have the same output value.

Domainx – coordinatesIndependent variable

Input

Rangey – coordinatesDependent variable

Output

How can I remember

Domain and Range?

NOTICEX comes before Y

&D (Domain) comes before R

(Range)X’s=DomainY’s= Range

How do I know it’s a function?

Look at the input and output table – Each input must have exactly one output.

Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

Vertical Line Test

Vertical Line Test:1. 2. 3.

Example 1:{(3, 2), (4, 3), (5, 4), (6, 5)}

function

Example 2:

function

Example 3:

relation

Example 4: ( x, y) = (student’s name, shirt color)

function

Example 5: Red Graph

relation

Function or Relation?

relation

Comic Strip Helpful Reminders

1. Do you have your system listed Example: y=4x + 5 and y=3x

-32. Did you solve your system in one of the three methods: elimination, substitution, graphing3. Is it neatly written?4. Do you have AT LEAST 6 slides?Due Wednesday at end of class