Let f(x) = x^3 - 5x^2 + 2x-7 and g(x) = f(4x). Which of the following describes

Question

Let f(x) = x^3 - 5x^2 + 2x-7 and g(x) = f(4x). Which of the following describes g as a function of f and gives the correct rule? vertical stretch; g(x) = 4x^3- 20x^2 + 8x - 28 vertical compression; g(x) = 64x^3 - 80x^2 + 8x - 7 horizontal compression; g(x) = 64x^3 - 80x^2 + 8x - 7 horizontal stretch; g(x) = 4x^3 - 20x^2 + 8x - 28 Let f(x) = x^3 + 2x^2 + 3x -10. Identify the function g that reflects 1 across the y-axis. g(x) = -x^3 - 2x^2 - 3x + 10 g(x) = -x^3 + 2x^2 - 3x + 10 g(x) = -x^3 - 2x^2 + 3x - 10 g(x) = -x^3 + 2x^2 - 3x - 10 Identify the function that vertically stretches f(x) = -2x^3 + 5 by a factor of 3 and shifts it 2 units left.

Explanation / Answer

f(x) = x^3 - 5x^2 + 2x - 7

g(x) = f(4x)

plug x = 4x in f(x)

g(x) = (4x)^3 - 5(4x)^2 + 2(4x) - 7

= 64x^3 - 80x^2 + 8x - 7 horizontal compression

option 3

2) f(x) = x^3 + 2x^2 + 3x - 10

reflection across y axis is given by f(x) = f(-x)

g(x) = (-x)^3 + 2(-x)^2 + 3(-x) +10

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

option 2

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