Question

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

$f\left(x\right)=x^4+2x+6$ ; vertical stretch by a factor of 2, followed by a translation 4 units right

$g\left(x\right)=$

Answer 1

First apply the vertical stretch: h(x)=2f(x)=2(x^4+2x+6).
Then translate 4 units right: replace x by x-4.

Thus
g(x)=2[(x-4)^4 + 2(x-4) + 6].

Expanded:
g(x)=2x^4 - 32x^3 + 192x^2 - 508x + 508.