Question

Write a rule for g​ that represents the indicated transformations of the graph of f.

Answer 1

The rule of g(x) is g(x) = 2 $(x-4)^{4}$ + 4(x - 4) + 12

Step-by-step explanation:

Let us revise some transformation

• If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
• If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k

∵ f(x) = $x^{4}$ + 2x + 6

∵ The graph of f(x) is stretched vertically by a factor of 2

- That means the y-coordinate of each point on the graph is multiplied

   by 2, then y = 2.f(x) as the 2nd rule above

∴ y = 2[ $x^{4}$ + 2x + 6]

∴ y = 2 $x^{4}$ + 4x + 12

∵ The graph of 2.f(x) is translated 4 units to the right

- That means substitute every x by (x - 4) as the 1st rule above

∴ g(x) = 2 $(x-4)^{4}$ + 4(x - 4) + 12

The rule of g(x) is g(x) = 2 $(x-4)^{4}$ + 4(x - 4) + 12

Learn more:

You can learn more about transformation in brainly.com/question/2451812

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