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The graph of y= (x^3) +6
is translated 4 units to the right.
The translated graph has equation y=f(x).
Work out f(x).

Give your answer in the form
x^3 + ax^2 + bx + c
where a, b and c are integers.

Respuesta :

semsee45

Answer:

[tex]y=x^3-12x^2+48x-58[/tex]

Step-by-step explanation:

Transformation Rules

[tex]f(x+a)=f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a)=f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

Given equation: [tex]y=x^3+6[/tex]

If the graph of the equation is translated 4 units to the right, then we replace [tex]x[/tex] with [tex](x-4)[/tex]:

[tex]\implies y=(x-4)^3+6[/tex]

[tex]\implies y=(x-4)(x-4)(x-4)+6[/tex]

[tex]\implies y=(x-4)(x^2-8x+16)+6[/tex]

[tex]\implies y=x^3-8x^2+16x-4x^2+32x-64+6[/tex]

[tex]\implies y=x^3-12x^2+48x-58[/tex]

Ver imagen semsee45

Answer:

  • f(x) = x³ - 12x² + 48x + 58

Step-by-step explanation:

Given

  • y = x³ + 6

Translating 4 units right

  • x → x - 4
  • f(x) = (x - 4)³ + 6
  • f(x) = x³ - 3(x)²(4) + 3(x)(4)² - (4)³ + 6
  • f(x) = x³ - 12x² + 48x - 64 + 6
  • f(x) = x³ - 12x² + 48x + 58

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