Question

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Answer 1

Answer:

1. g(x) = 2|x|
2. g(x) = -2|x|
3. g(x) = -2|x| -3
4. g(x) = -2|x-1| -3

Step-by-step explanation:

1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...

  g(x) = 2|x|

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2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.

  g(x) = -2|x|

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3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.

  g(x) = -2|x| -3

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4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...

  g(x) = -2|x -1| -3