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15 January, 06:43

The function g (x) = x^2+3. The function f (x) = g (x+2). The function f (x) is shifted horizontally how many places to where? The function f (x) is shifted vertically how many places where?

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  1. 15 January, 07:25
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    The function f (x) is shifted 2 units to the left and 3 units up

    Step-by-step explanation:

    * Lets revise the translation of a function

    - If the function f (x) translated horizontally to the right

    by h units, then the new function g (x) = f (x - h)

    - If the function f (x) translated horizontally to the left

    by h units, then the new function g (x) = f (x + h)

    - If the function f (x) translated vertically up

    by k units, then the new function g (x) = f (x) + k

    - If the function f (x) translated vertically down

    by k units, then the new function g (x) = f (x) - k

    * Lets solve the problem

    ∵ g (x) = x² + 3

    ∵ f (x) = g (x + 2)

    - Lets find g (x + 2) by replacing x in g (x) by (x + 2)

    ∵ g (x) = x² + 3

    ∴ g (x + 2) = (x + 2) ² + 3

    ∵ f (x) = g (x + 2)

    ∴ f (x) = (x + 2) ² + 3

    - The parent function of f (x) is x²

    ∵ x² changed to (x + 2) ²

    - Use the rules above

    ∴ f (x) is translated 2 units to the left

    ∵ (x + 2) ² added by 3

    - Use the rules above

    ∴ f (x) is translated 3 units up

    * The function f (x) is shifted 2 units to the left and 3 units up
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