By analyzing the graph of the transformed function, we can see that:
g(x) = 2*|x - 2| - 4
<h3>
How to get the function g(x)?</h3>
In the image we have two graphs, the yellow one is the graph of g(x).
First, analyzing the vertex we can see the translation used, you need to remember:
<u>Horizontal translation:</u>
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
- If N is positive, the shift is to the left.
- If N is negative, the shift is to the right.
<u>Vertical translation:</u>
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
- If N is positive, the shift is upwards.
- If N is negative, the shift is downwards.
We can see that the new vertex is at (2, -4), so the translation is 2 units to the right and 4 units down, then we have:
g(x) = |x - 2| - 4
Now, you also can see that the yellow function is narrower, such that for each increase in the x-unit, we have an increase of 2 in the y-axis, then we need to multiply by 2 the absolute value part:
g(x) = 2*|x - 2| - 4
This is the transformed function.
If you want to learn more about transformations, you can read:
brainly.com/question/4289712
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eliminates -1/6 from being another solution.