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Given the function f(x) = |x|, shift 3 units to the left and shift downward 4 units.

User Tjans
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The equation for the final transformed graph is:

f(x) = x - 1, if x ≥ -6

-x - 4, if x < -6

To find the equation for the final transformed graph, we need to apply the given transformations to the function f(x) = |x| in the given order. The transformations are:

Shift 3 units to the left

Shift downward 4 units

To shift the graph 3 units to the left, we need to replace x with (x + 3) in the function. This gives us:

f(x) = |x| → f(x + 3) = |x + 3|

To shift the graph downward 4 units, we need to subtract 4 from the function. This gives us:

f(x + 3) = |x + 3| → f(x + 3) - 4 = |x + 3| - 4

Simplifying the expression |x + 3| - 4, we get:

|x + 3| - 4 =

x + 3 - 4, if x + 3 ≥ 0

-(x + 3) - 4, if x + 3 < 0

Combining the two cases, we get:

f(x + 3) - 4 =

x - 1, if x ≥ -3

-x - 7, if x < -3

Therefore, the equation for the final transformed graph is:

f(x) = x - 1, if x ≥ -6

-x - 4, if x < -6

Complete question:

A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. Given the function f(x) = |x|, shift 3 units to the left and shift downward 4 units.

User Ahmad ElMadi
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7.9k points

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