M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
Math 3 Unit 5, Rational Functions
Recall: Direct Variation
y = kx
Lesson 1 "Inverse Variation"
Will know: • Division by zero is not possible.
• Interval notation to express domain.
• Model inverse variation
• Identify direct, inverse, compound and joint variation.
November 07, 2016
Inverse Variation
y = k/x
xy = k
Will do:
• Translate an inverse variation.
• Determine the domain
• Discuss asymptotes and points of discontinuity.
• Graph a rational function using asymptotes
• I will find the constant of inverse variation given a point solution set.
• I will identify if a set of data is direct variation, inverse variation or neither.
Sep 25­9:06 AM
Suppose y varies inversely with x, and goes through the point (3,­5). Find the function that models this inverse variation.
Dec 13­8:58 PM
You try
Suppose that x and y vary inversely, and x = 0.3 when y = 1.4. Write the function that models the inverse variation.
1 Enter the value of k into you clicker?
Dec 13­9:01 PM
Dec 13­9:05 PM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
November 07, 2016
@ The Movies
PH Videos:
• Using inverse variations
Dec 13­9:08 PM
2 Choose the type of variation.
B Inverse
A Direct
C Neither
page 480
y/x is a constant ∴ it is direct variation, y = kx.
xy is a constant ∴ it is inverse variation, y = k/x
It is neither direct or indirect variation
Dec 13­9:14 PM
• "Varies Inversely": the variable goes in the
denominator
• "Varies Directly": the variable goes in the numerator
• "Varies Jointly": the product of the two variables goes
in the numerator
Dec 13­9:23 PM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
@ The Movies
PH Videos:
• Using joint and other
variations
November 07, 2016
Prentice Hall Algebra On Line Resources
Go to "http://www.phschool.com/" then enter Web Code agk­0099
Homework
p481, #1-23 odd
p482 #43-51
p481, #1-23 odd
p481, #1-23 odd
Jan 4­3:07 PM
Dec 13­9:35 PM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
p481, #1-23 odd
Jan 4­3:07 PM
November 07, 2016
p481, #1-23 odd
Jan 4­3:09 PM
Math 3 Unit 5, Rational Functions
Lesson 2 "Graphing Inverse Functions"
p482 #43-51
WALT: We are learning to: • Graph inverse variations
• Translate inverse variations
WIMD: What I must do:
• I will sketch the parent graph of inverse variations and identify the domain, range and asymptotes.
• I will translate and sketch a graph of an inverse function by analyzing it's constants of translation, a, h, and k
Dec 13­9:29 PM
Sep 25­9:06 AM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
Graph y = 1/x
Graph y = 9/x
November 07, 2016
Graph y = 25/x
notice the asymptotes at
y = 0 and x = 0
Domain:
Range:
For y = a/x, a stretches or compresses our base graph along the axis of symmetry y=x.
Notice the intersection of the line of symmetry, y=x and the closest point on the line to the origin. They are at coordinates (√a, √a) and (-√a, -√a)
Dec 14­7:24 PM
Dec 14­7:47 PM
For y = ­a/x the graph "flips."
Dec 14­7:37 PM
Dec 14­7:42 PM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
Dec 14­7:53 PM
@ The Movies
PH Videos:
• Graphing reciprocal
functions
November 07, 2016
Dec 14­7:58 PM
Graph:
Horizontal asymptote:
Vertical asymptote:
"Vertices":
Dec 14­8:00 PM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
November 07, 2016
Prentice Hall Algebra On Line Resources
Go to "http://www.phschool.com/" then enter Web Code agk­0099
Homework
p488, #10-24
you try...
Write an equation for the translation of y = that is 4 units left
and 5 units up.
Dec 14­8:11 PM
Dec 14­8:18 PM
Dec 14­8:18 PM
M3U5L01 and L02 9.1 and 9.2 Inverse Variation .notebook
Dec 14­8:19 PM
Nov 7­8:18 AM
November 07, 2016
Nov 7­8:17 AM
Attachments
Prentice Hall Algebra On lIne Resources