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13 September, 08:44

The graph shows the function f (x) = (2.5) x was horizontally translated left by a value of h to get the function g (x) = (2.5) x-h.

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  1. 13 September, 12:19
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    F (x) = (2.5) ^x

    g (x) = (2.5) ^ (x - h)

    You should know that when you add a constant to the argument of a function the graph moves left h unit, this is the graph of f (x + h) is the graph of f (x) shifted h units leftward.

    You can make this table for f (x) and g (x)

    x f (x) = (2.5) ^x g (x) [from the graph]

    -3 (2.5) ^ (-3) = 0.064 0.4

    -2 (2.5) ^ (-2) = 0.16 1

    -1 (2.5) ^ (-1) = 0.4 2.5

    0 1

    1 2.5

    2 (2.5) ^2 = 6.25

    From that table you can see that:

    g (-3) = f (-1)

    g (-2) = f (0)

    g (-1) = f (1)

    And you can infere that g (x) = f (x + 2)

    Then, g (x) = (2.5) ^ (x - h) = (2.5) ^ (x + 2)

    Which implies that x - h = x + 2 = > h = - 2.

    Then the answer is h = - 2
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