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What's the equation:
f(x)=x^2, horizontally stretched by a factor of 1/3, reflected vertically and horizontally, translated 11 units to the left and 4 units up

Respuesta :

Using shifting concepts, it is found that the function g is:

[tex]g(x) = -9x^2 - 198x - 1085[/tex]

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  • The parent function is [tex]f(x) = x^2[/tex].

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  • Horizontally stretching a function by a factor of b is the finding [tex]f(\frac{x}{b})[/tex].
  • Thus, horizontally stretching by a factor of 1/3, we have:

[tex]g(x) = f(\frac{x}{\frac{1}{3}}) = f(3x) = (3x)^2 = 9x^2[/tex]

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  • Reflecting vertically is finding [tex]-f(x)[/tex]
  • Reflecting horizontally is finding [tex]f(-x)[/tex].

Thus:

[tex]g(x) = -9(-x)^2 = -9x^2[/tex]

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  • Translating a units to the left is finding [tex]f(x + a)[/tex], thus:
  • Translating 11 units to the left is finding [tex]f(x + 11)[/tex], thus:

[tex]g(x) = -9(x + 11)^2 = -9(x^2 + 22x + 121) = -9x^2 - 198x - 1089[/tex]

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  • Shifting a units up is finding [tex]f(x) + a[/tex], thus:
  • 4 units up is finding [tex]f(x) + 4[/tex], thus:

[tex]g(x) = -9x^2 - 198x - 1089 + 4 = -9x^2 - 198x - 1085[/tex]

A similar problem is given at https://brainly.com/question/23325498

Answer:

Step-by-step explanation:

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