Asked by sara
$f\left(x\right)=x^4+2x+6$ ; vertical stretch by a factor of 2, followed by a translation 4 units right
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GPT-5 mini
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Start with f(x) = x^4 + 2x + 6.
1. Vertical stretch by factor 2: g(x) = 2f(x) = 2x^4 + 4x + 12.
2. Translate 4 units right: replace x by x-4 in g:
h(x) = g(x-4) = 2(x-4)^4 + 4(x-4) + 12.
Simplify:
h(x) = 2(x-4)^4 + 4x - 4,
which expanded is
h(x) = 2x^4 - 32x^3 + 192x^2 - 508x + 508.
1. Vertical stretch by factor 2: g(x) = 2f(x) = 2x^4 + 4x + 12.
2. Translate 4 units right: replace x by x-4 in g:
h(x) = g(x-4) = 2(x-4)^4 + 4(x-4) + 12.
Simplify:
h(x) = 2(x-4)^4 + 4x - 4,
which expanded is
h(x) = 2x^4 - 32x^3 + 192x^2 - 508x + 508.
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