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Algebra

Adding functionsAlgebra

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Multiplying functionsAlgebra

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Polynomial synthetic division - Home
- AU Year 12 Maths
- Functions

Still Confused?

Try reviewing these fundamentals first

Algebra

Adding functionsAlgebra

Subtracting functionsAlgebra

Multiplying functionsAlgebra

Dividing functionsAlgebra

Polynomial long divisionAlgebra

Polynomial synthetic division Still Confused?

Try reviewing these fundamentals first

Algebra

Adding functionsAlgebra

Subtracting functionsAlgebra

Multiplying functionsAlgebra

Dividing functionsAlgebra

Polynomial long divisionAlgebra

Polynomial synthetic division Nope, got it.

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Get Started Now- 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

Basic Concepts: Adding functions, Subtracting functions, Multiplying functions, Dividing functions, Polynomial long division, Polynomial synthetic division

Difference function:

Quotient function:

- Introduction
__Introduction 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 $f(x) = 2x^{2}$ 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 $f(x) = 2x^{2} + x - 3$ and $g(x) = x^{2} + x + 13$.

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:

$C(n) = 1.2n + \frac{150,000}{n}$ 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.

2.

Functions

2.1

Function notation

2.2

Operations with functions

2.3

Adding functions

2.4

Subtracting functions

2.5

Multiplying functions

2.6

Dividing functions

2.7

Composite functions

2.8

Inequalities of combined functions

2.9

Inverse functions

2.10

One to one functions

2.11

Difference quotient: applications of functions