Using translation concepts, the graph of f(x) is given at the end of the answer.
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The parent absolute value function is given by:
f(x) = |x|
Which has the graph in the format of a V centered at the origin.
The translated function is given by:
g(x) = -1/2|x + 4| + 2.
The translations are as follows:
- Reflection over the x-axis, due to the multiplication by the negative number, thus the V is pointing down now.
- Vertical compression by a factor of 2, due to the division by 2.
- Shift left of 4 units, as x -> x + 4.
- Shift up of 2 units, as y -> y + 2.
Due to the last two translations, the graph is now centered at (-4,2) and is given at the end of the answer.
More can be learned about translation concepts at https://brainly.com/question/4521517
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