Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=x^4+2x+6; vertical stretch by a factor of 2, followed by a translation 4 units right.

g(x)=?

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) = [tex]x^{4}[/tex] + 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[ [tex]x^{4}[/tex] + 2x + 6]

∴ y = 2 [tex]x^{4}[/tex] + 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 [tex](x-4)^{4}[/tex] + 4(x - 4) + 12

The rule of g(x) is g(x) = 2 [tex](x-4)^{4}[/tex] + 4(x - 4) + 12

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Write a rule for g​ that represents the indicated transformations of the graph of f. f(x)=x^4+2x+6; vertical stretch by a factor of 2, followed by a translation 4 units right. g(x)=?