Function notation

Lessons

• Introduction
  Introduction to function notations

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• 1.
  If $f(x) = 5x^2-x+6$ find the following
  a)

  ${f(\heartsuit)}$
  
  
  b)

  ${f(\theta)}$
  
  
  c)

  ${f(3)}$
  
  
  d)

  ${f(-1)}$
  
  
  e)

  ${f(3x)}$
  
  
  f)

  ${f(-x)}$
  
  
  g)

  ${f(3x-4)}$
  
  
  h)

  ${3f(x)}$
  
  
  i)

  ${f(x)-3}$
  
  

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• 2.
  If f(x) = 6 - 4x, find:
  a)

  f(3)
  
  
  b)

  f(-8)
  
  
  c)

  f(-2/5)
  
  

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• 3.
  If f(r) = $2\pi r^2h$, find f(x+2)

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• 4.
  If ${f(x) = \sqrt{x},}$ write the following in terms of the function ${f.}$
  a)

  ${\sqrt{x}+5}$
  
  
  b)

  ${\sqrt{x+5}}$
  
  
  c)

  ${\sqrt{2x-3}}$
  
  
  d)

  ${-8\sqrt{x}}$
  
  
  e)

  ${-8\sqrt{2x-3}}$
  
  
  f)

  $4\sqrt{x^{5}+9}-1$
  
  

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• 5.
  If f(x) = -3x + 7, solve for x if f(x) = -15

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• 6.
  The temperature below the crust of the Earth is given by C(d) = 12d + 30, where C is in Celsius and d is in km.
  i.) Find the temperature 15 km below the crust of the Earth.
  ii.) What depth has a temperature of $186^\circ$C?
  

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