7. Use the facts and graph below to write the equation for g(x) Step 1: Start with the equation f(x) = |x|. Write the equation for the graph of g(x) that has been stretched vertically by a factor of 2.
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been reflected, or flipped, over the x-axis.
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted down 3 units.
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.

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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

9

step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)