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marin [14]
2 years ago
5

Given the parent function f(x)=|x|, write the equation of the function g(x) whose graph is pictured

Mathematics
1 answer:
kenny6666 [7]2 years ago
5 0

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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