Question

7. Use the facts and graph below to write the equation for g(x)

Answer 1

9514 1404 393

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. Multiplying the function by a constant stretches the graph by that constant. Here, you want a stretch factor of 2, so you have ...

  g(x) = 2f(x) = 2|x|

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2. Negating a function causes its graph to be reflected over the x-axis. That makes your second function look like ...

  g(x) = -2|x|

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3. Subtracting 3 from the function value shifts its location on a graph down by 3 units. Your third function will be ...

  g(x) = -2|x| -3

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4. Subtracting a constant from the x-value causes the graph of the function to be shifted right by that amount. Here you want a right shift of 1 unit, so your function is ...

  g(x) = -2|x -1| -3