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In complete sentences, determine the effects of the transformations for this functions and describe it. f(x)= | x+2 |

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Final answer:

The effect of the transformation on the function f(x)=|x+2| is a horizontal shift 2 units to the left, from its original position, and is therefore a graph of the absolute value function between x = -2 and x = 18.

Step-by-step explanation:

To determine the effects of the transformations on the function f(x) = |x + 2|, we first recognize that the absolute value function f(x) = |x| is a V-shaped graph with its vertex at the origin. When we introduce a transformation such as f(x) = |x + 2|, we are applying a horizontal shift to the graph of the absolute value function. Specifically, the graph will shift 2 units to the left because the transformation involves x + 2 inside the absolute value. This can be seen as the effect of the transformation f(x + d), which shifts the function f 2 units in the negative x-direction.

Moreover, since the graph is restricted with 0 ≤ x ≤ 20, the graph of f(x) will only span from x = -2 to x = 18, instead of the usual infinite extent in both directions.

Overall, the effect of the transformation applied to the absolute value function is a horizontal shift to the left by 2 units, adjusting the domain of the function to match the specified range of x.

User Ilay Zeidman
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