Inequalities of combined functions

Lessons

• Introduction
  Introduction to inequalities of combined functions

  i. What are inequalities of combined functions?

  ii. How many ways can it be solved?

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• 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 which

  i. $f(x)$ > $g(x)$

  ii. $g(x)$ > $f(x)$

  
  

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• 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 which

  i. $f(x)$ > $g(x)$

  ii. $g(x)$ > $f(x)$

  
  

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• 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. $g(x)$ > $f(x)$

  
  

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• 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 which

  i. $f(x)$ > $g(x)$

  ii. $g(x)$ > $f(x)$

  
  

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• 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.
  
  

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