describe the transformation that were applied to the following parent function: f(x) = 2|x+4|

shift left 4, dilate vertically by 2

Well, let me put on my clown nose and break it down for you. The parent function is like the original recipe, and we're adding some fun to it. Starting with the function f(x) = |x|, the transformation applied here is multiplying the whole thing by 2. So now we have f(x) = 2|x|.

But wait, there's more! We're not done yet. Next, we're adding some extra spice by shifting the function horizontally. The "+4" inside the absolute value means we're moving the whole graph 4 units to the left. So now we have f(x) = 2|x+4|.

So to sum it up, we have the original function dressed up with a multiplication by 2 and a horizontal shift of 4 units to the left. Voila! A transformed function with a touch of clown magic!

To describe the transformations applied to the parent function f(x) = 2|x|, we need to consider the effect of the expression inside the absolute value and any coefficients or constants outside the absolute value.

1. Vertical Shift:
The function f(x) = 2|x| has a vertical shift of 0 units, meaning it passes through the origin (0, 0). However, in the given function f(x) = 2|x+4|, the expression inside the absolute value introduces a horizontal shift of 4 units to the left.

2. Horizontal Shift:
The expression |x+4| introduces a horizontal shift of 4 units to the left. So, the graph of f(x) = 2|x+4| is shifted to the left by 4 units compared to the graph of f(x) = 2|x|.

3. Vertical Stretch/Compression:
The function f(x) = 2|x| has a vertical stretch factor of 2, meaning it is stretched vertically compared to the parent absolute value function f(x) = |x|. In the given function f(x) = 2|x+4|, this vertical stretch factor of 2 remains unchanged.

Overall, the transformation applied to the parent function f(x) = 2|x| to get the function f(x) = 2|x+4| involves a horizontal shift of 4 units to the left and no changes in vertical stretching.

To describe the transformations applied to the parent function f(x) = 2|x|, we need to understand the effects of each component of the function separately.

First, let's start with the absolute value function |x|. The absolute value function takes any value of x and returns its distance from zero. It always gives you a positive value or zero, regardless of the input's sign.

Now, looking at the transformed function f(x) = 2|x+4|, we can identify the following transformations:

1. Vertical Stretch/Compression: The coefficient "2" before the absolute value, multiplies every output value of the function by 2, which stretches the graph vertically by a factor of 2. If the coefficient were a fraction, it would compress the graph.

2. Horizontal Translation: The "+4" inside the absolute value function causes a horizontal shift to the left by 4 units since it is subtracted from x. Positive values inside the absolute value function shift the graph left, while negative values shift it right. In this case, it shifted to the left by 4 units.

3. Vertical Translation: There is no constant term outside the absolute value function, so there is no vertical translation in this case.

To summarize, the transformations applied to the parent function f(x) = 2|x| to get f(x) = 2|x+4| are a vertical stretch by a factor of 2, a horizontal translation to the left by 4 units, and no vertical translation.