Let f(x) = x^3 + 2x^2 + 7x - 11 and g(x) = f(x - 4). Which of the following desc

Question

Let f(x) = x^3 + 2x^2 + 7x - 11 and g(x) = f(x - 4). Which of the following describes g as a function of f and gives the correct rule? horizontal compression; g(x) = 4x^3 - 40x^2 + 156x - 71 vertical translation; g(x) = x^3 + 2x^2 + 7x - 11 vertical compression; g(x) = 4x^3 - 40x^2 + 156x - 284 horizontal translation; g(x) = x^3 - 10x^2 + 39x - 71 The table shows the numbers of cars manufactured by a company for selected years. Identify a polynomial function for cars manufactured in thousands where x represents the years since 1990. P(x) = 0.5x^3 + 0.2x^2 + 0.3x + 0.4 P(x) = 0.5x^3 + 0.5x^2 + 0.4x + 0.4 P(x) = 0.2x^3 + 0.5x^2 + 0.4x + 0.3 P(x) = 0.2x^3 + 0.2x^2 + 0.3x + 0.3

Explanation / Answer

f(x) = x^3 + 2x^2 + 7x - 11

g(x) = f(x-4)

plug x = x-4 in f(x)

g(x) = (x-4)^3 + 2(x-4)^2 + 7(x-4) - 11

= x^3-12x^2+48x-64 + 2(x^2 + 16 - 8x ) + 7x - 28 - 11

= x^3 -10x^2 + 39x - 71

horizontal translation and g(x) = x^3 -10x^2 + 39x - 71

option 4

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