Inequalities of combined functions

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Intros

Lessons

Introduction to inequalities of combined functions
i. What are inequalities of combined functions?

ii. How many ways can it be solved?

Examples

Lessons

Evaluating Inequalities of Combined Functions by Comparing the Functions Graphically
Let $f(x) = 2x^{2}$ and $g(x) = 3x + 2$ .
1. Graph the functions on the same set of axes. Identify the points of intersection.
2. Illustrate the regions for which
  i. $f(x)$ > $g(x)$
  
  ii. $g(x)$ > $f(x)$
Evaluating Inequalities of Combined Functions by Analyzing the Difference Function
Let $f(x) = 2x^{2} + x - 3$ and $g(x) = x^{2} + x + 13$ .
1. Graph the difference function.
2. Illustrate the regions for which
  i. $f(x)$ > $g(x)$
  
  ii. $g(x)$ > $f(x)$
Let $f(x) = (x-3)(x+5)$ $f (x) = (x - 3) (x + 5)$ and $g(x) = (x+1)(x-4)$ $g (x) = (x + 1) (x - 4)$
1. Graph the difference function.
2. Illustrate the regions for which
  i. $f(x)$ > $g(x)$
  
  ii. $g(x)$ > $f(x)$
Evaluating Inequalities of Combined Functions by Analyzing the Quotient Function
Let $f(x) = (x+3)^{6}$ and $g(x) = (x+3)^{4}$
1. Graph the quotient function.
2. Illustrate the regions for which
  i. $f(x)$ > $g(x)$
  
  ii. $g(x)$ > $f(x)$
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.
1. Use graphing technology to graph C( $n$ ). What is the domain of this function?
2. Determine the number of phones that can be made if Nick wants to keep the cost below $1000.

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