2 Points
f(x) = x2 - 3x - 2 is shifted 4 units left. The result is g(x). What is 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 the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)

∵ f(x) = x² - 3x - 2

∵ f(x) is shifted 4 units left

- That means add 4 to each x in the function f(x)

∴ g(x) = (x + 4)² - 3(x + 4) - 2

Simplify it by solving the bracket of power two and open the other

bracket by multiply it by 3 and adding the like terms

∵ (x + 4)² = (x)(x) +2(x)(4) + (4)(4)

∴ (x + 4)² = x² + 8x + 16

∵ 3(x + 4) = 3x + 12

∴ g(x) = [x² + 8x + 16] - [3x + 12] - 2

∴ g(x) = x² + 8x + 16 - 3x - 12 - 2

- Add like terms

∴ g(x) = x² + (8x - 3x) + (16 - 12 - 2)

∴ g(x) = x² + 5x + 2

g(x) = x² + 5x + 2

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