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3 June, 01:32

Function f, shown below, is translated down 3 units and left 4 units to create function g. f (x) = 3|x-2|-5. Fill in the values of a, h, and k to write function g.

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  1. 3 June, 02:20
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    The graphs of the functions can be transformed, obtaining related functions.

    We consider two kinds of transformations.

    Vertical and horizontal displacements: It is assumed that c is a positive constant, ie c> 0 and y = f (x) then

    y = f (x) + c moves the graph c units up.

    y = f (x) - c moves the graph c units down.

    y = f (x + c) shifts the graph c units to the right.

    y = f (x - c) shifts the graph c units to the left.

    We have then:

    f (x) = 3 | x-2 | - 5

    Is down 3 units

    f (x) = 3 | x-2 | - 5 - 3

    and left 4 units

    f (x) = 3 | (x-4) - 2 | - 5 - 3

    Rewriting

    g (x) = 3lx-6l-8

    Answer:

    g (x) = 3lx-6l-8
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