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19 June, 13:53

The parent function y = |x| stretched vertically by a factor of 2, shifted left 3 units and down 4 units

whats the equation?

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  1. 19 June, 14:02
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    Hello!

    Let's go through some formula to distinguish the changes that happen to a graph's equation when they are transformed.

    Vertical shifts have this type of formula:

    f (x) + k → up k units and f (x) - k → down k units

    Horizontal shifts have this type of formula:

    f (x + k) → left k units and f (x - k) → right k units

    Reflections have this type of formula:

    -f (x) → reflect over x-axis and f (-x) → reflect over y-axis

    Vertical stretches have this type of formula:

    a · f (x) where a > 1

    Vertical compressions have this type of formula:

    a · f (x) where a < 1

    Horizontal stretches have this type of formula:

    f (a · x) where a > 1

    Horizontal compressions have this type of formula:

    f (a · x) where a < 1

    With that in mind, we can write our transformed absolute value function.

    Since the equation is vertically stretched by a factor of 2, a = 2.

    y = 2|x|

    Also, since the function is shifted left 3 units, k = - 3.

    y = 2|x + 3|

    Finally, the function is also shifted down 4 units, so k = - 4.

    y = 2|x + 3| - 4

    Therefore, the equation is y = 2|x + 3| - 4.
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