By analyzing the graph of the transformed function, we can see that:
g(x) = 2*|x - 2| - 4
How to get the function g(x)?
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:
Horizontal translation:
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.
Vertical translation:
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:
https://brainly.com/question/4289712
