Math

QuestionIdentify the parent function and transformations for: y=2x+4+4y=2|x+4|+4.

Studdy Solution

STEP 1

Assumptions1. The given function is y=x+4+4y=|x+4|+4 . We are asked to identify the parent function and all transformations.

STEP 2

The parent function is the simplest form of the given function. In this case, the parent function is y=xy=|x|. This is because the absolute value function, y=xy=|x|, is the simplest form of the given function.

STEP 3

To identify the transformations, we need to compare the given function with the parent function. The general form of a transformed absolute value function is y=abxh+ky=a|bx-h|+k.

STEP 4

In the general form, aa represents the vertical stretch or shrink, bb represents the horizontal stretch or shrink, hh represents the horizontal shift, and kk represents the vertical shift.

STEP 5

Comparing the given function y=2x+4+4y=2|x+4|+4 with the general form, we can see that a=2a=2, b=1b=1, h=4h=-4, and k=4k=4.

STEP 6

The value of a=2a=2 indicates a vertical stretch by a factor of2. This means the graph of the function is stretched vertically by a factor of2.

STEP 7

The value of b=1b=1 indicates there is no horizontal stretch or shrink.

STEP 8

The value of h=4h=-4 indicates a horizontal shift4 units to the left. This means the graph of the function is shifted4 units to the left.

STEP 9

The value of k=4k=4 indicates a vertical shift4 units up. This means the graph of the function is shifted4 units up.
So, the parent function is y=xy=|x| and the transformations are a vertical stretch by a factor of2, a horizontal shift4 units to the left, and a vertical shift4 units up.

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