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Which transformation(s) were used to go from the parent graph (red) to the transformed graph (blue)? Check all that apply!

Which transformations were used to go from the parent graph red to the transformed graph blue Check all that apply class=

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2 Answers:

Choice B) Shift down

Choice C) Shift right

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Explanation:

Start with the point (-2,-4). Let's try to move it to (2, -9)

To do so, we need to shift down and to the right (in either order).

Specifically we shift 4 units to the right to go from x=-2 to x=4

Note how x=-2 moves to x+4 = -2+4 = 2

Also, we shift 5 units down. We have y = -4 turn into y = -9 as shown below

y ---> y-5 = -4-5 = -9

So the translation rule is [tex](x,y) \to (x+4,y-5)[/tex]

Let's see what happens when we apply the translation rule to (2,4)

[tex](x,y) \to (x+4, y-5)\\\\(2,4) \to (2+4, 4-5)\\\\(2,4) \to (6, -1)\\\\[/tex]

which is the other endpoint of the blue segment. This shows that the translation rule works for (2,4) to move to (6,-1)

We do not apply any dilations. The red and blue segments are the same length because translations preserve distance. All we're effectively doing is moving the red segment to land on the blue segment. This means no vertical or horizontal stretches are done. The same can be said about compressions as well.

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