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Inequalities of combined functions
- Intro Lesson4:38
- Lesson: 1a10:32
- Lesson: 1b2:45
- Lesson: 2a5:44
- Lesson: 2b2:31
- Lesson: 3a5:20
- Lesson: 3b1:43
- Lesson: 4a6:39
- Lesson: 4b4:32
- Lesson: 5a5:31
- Lesson: 5b12:01
Inequalities of combined functions
Basic Concepts: Adding functions, Subtracting functions, Multiplying functions, Dividing functions, Polynomial long division, Polynomial synthetic division
Lessons
Difference function:
Quotient function:
- IntroductionIntroduction to inequalities of combined functions
i. What are inequalities of combined functions?
ii. How many ways can it be solved?
- 1.Evaluating Inequalities of Combined Functions by Comparing the Functions Graphically
Let f(x)=2x2 and g(x)=3x+2.
a)Graph the functions on the same set of axes. Identify the points of intersection.b)Illustrate the regions for whichi. f(x) > g(x)
ii. g(x) > f(x)
- 2.Evaluating Inequalities of Combined Functions by Analyzing the Difference Function
Let f(x)=2x2+x−3 and g(x)=x2+x+13.
a)Graph the difference function.b)Illustrate the regions for whichi. f(x) > g(x)
ii. g(x) > f(x)
- 3.Let f(x)=(x−3)(x+5) and g(x)=(x+1)(x−4)a)Graph the difference function.b)Illustrate the regions for which
i. f(x) > g(x)
ii. g(x) > f(x)
- 4.Evaluating Inequalities of Combined Functions by Analyzing the Quotient Function
Let f(x)=(x+3)6 and g(x)=(x+3)4
a)Graph the quotient function.b)Illustrate the regions for whichi. f(x) > g(x)
ii. g(x) > f(x)
- 5.Application of Inequalities of Combined Functions
Nick is starting his own phone company. The cost of making and storing phones can be modelled by the function:
C(n)=1.2n+n150,000 where n = number of phones. The storage capacity of the company's warehouse is 500 units.
a)Use graphing technology to graph C(n). What is the domain of this function?b)Determine the number of phones that can be made if Nick wants to keep the cost below $1000.
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7.
Functions
7.1
Function notation
7.2
Operations with functions
7.3
Adding functions
7.4
Subtracting functions
7.5
Multiplying functions
7.6
Dividing functions
7.7
Composite functions
7.8
Inequalities of combined functions
7.9
Inverse functions
7.10
One to one functions
7.11
Difference quotient: applications of functions