The cost of manufacturing x refrigerators is given by the function f(x)=2x^2+6000. If the cost doubles fr the year 2011 owing to higher raw material prices, which transformation will result in the graph of f(x)? CHOICES: Reflection, Vertical Stretch, Vertical Shrink, Horizontal Shrink, or Horizontal Stretch

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whovian2536 whovian2536

18-05-2018
Mathematics

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The cost of manufacturing x refrigerators is given by the function f(x)=2x^2+6000. If the cost doubles fr the year 2011 owing to higher raw material prices, which transformation will result in the graph of f(x)? CHOICES: Reflection, Vertical Stretch, Vertical Shrink, Horizontal Shrink, or Horizontal Stretch

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JeanaShupp JeanaShupp · Answer 1 · 2019-06-04T07:28:43+02:00

Answer: Vertical Stretch

Step-by-step explanation:

Given: The cost of manufacturing x refrigerators is given by the function :[tex]f(x)=2x^2+6000[/tex]

If the cost doubles fr the year 2011 owing to higher raw material prices, then we multiply the given function by 2, then we get a new function :

[tex]g(x)=2(2x^2+6000)=4x^2+12000[/tex] which represents a vertical stretch in the graph.

∵ 2 is a positive constant greater than 1 which is multiplied to the parent function f(x). So by the definition of vertical stretch the parent function will be vertically stretched .