september 27 th
DESCRIPTION
Monday, September 30 th. Please Complete Warm Up. Warm-Up. September 27 th. Solve and graph -10 < 2x – 5 ≥ 12 Solve for L: m=2∏²-2∏L. Functions vs Relations. Coordinate Plane: Graph formed by the intersection of 2 number lines (axes) Origin: The point of intersection; (0,0) - PowerPoint PPT PresentationTRANSCRIPT
September 27th
Please Complete Warm Up
1. Solve and graph -10 < 2x – 5 ≥ 12
2. Solve for L: m=2∏²-2∏L
Warm-Up
Monday, September 30th
Functions vs Relations
Vocabulary•Coordinate Plane: Graph formed by the intersection of 2 number lines (axes)
•Origin: The point of intersection; (0,0)•X-axis: Horizontal Number Line•Y-axis: Vertical Number Line•Ordered Pair: Points on a graph (x-coordinate, y-coordinate)
Quadrants
Do you Remember How to Graph?!?!?!?
•X coordinate: Tells me how many units to move left of right
Negative: left Positive: right•Y Coordinate: Tells
me how many units to move up or down
Negative: downPositive: up
GraphA: (3,5) B: (-2, 4)
C: (3,-6)
1. EQuadrant ll
2. Fno quadrant (y-axis)
3. GQuadrant l
4. HQuadrant lll
•E•F
•H
•Gx
y
Name that Quadrant!
What is a Function? • It’s like a machine! You INPUT a number to
get an OUTPUT• Input: The value substituted for x•Output: 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
Relation•Any set of input that has an output•Input and output values are ordered
Function•A relation where EACH input has exactly ONE output
•Each element from the domain is paired with one and only one element from the range
•Different input values can have the same output value.
Domain•x – coordinates•Independent variable•Input
Range•y – coordinates•Dependent 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
Function Notation
Function form of an equation• A way to name a function
• f(x) is a fancy way of writing “y” in an equation.
• Pronounced “f of x”
Evaluating Functions
Evaluating a functionf(x) = 2x – 3 when x = -2
f(-2) = - 4 – 3 f(-2) = - 7
Tell me what you get when x is -2.
f(-2) = 2(-2) – 3
Evaluating a functionf(x) = x2 – 2x + 3 find f(-3)
f(-3) = 9 + 6 + 3f(-3) = 18
Tell me what you get when x is -3.
f(-3) = (-3)2 – 2(-3) + 3
Domain and Range
• Only list repeats once• Put in order from
least to greatest
What are the Domain and Range?
x 1 2 3 4 5 6y 1 3 6 10 15 21
Domain: Range:
{1, 2, 3, 4, 5, 6}{1, 3, 6, 10, 15,
21}
What are the Domain and Range?
Domain:
Range:
{0, 1, 2, 3, 4}
{1, 2, 4, 8, 16}
15. What are the Domain and Range?
Domain:
Range:
x ≥ -1
All Real Numbers
Homework/Classwork
Function Practice
Worksheet