Did I Transform This Equation Correctly?

[aisha]

The equation of the image is y=-2sqrt(3x-12)-5
It said describe the series of transformations so i rewrote the eqn into the form af[k(x-p)]+q
I got -2sqrt(3(x-(-4))-5 is this correct?

Vertical stretch by a factor of 2 horizontal compression by a factor of 1/3, reflection in the x axis, horizontal translation 4 units left and vertical translation 5 units down?

 

[apchemstudent]

The equation of the image is y=-2sqrt(3x-12)-5
It said describe the series of transformations so i rewrote the eqn into the form af[k(x-p)]+q
I got -2sqrt(3(x-(-4))-5 is this correct?

Vertical stretch by a factor of 2 horizontal compression by a factor of 1/3, reflection in the x axis, horizontal translation 4 units left and vertical translation 5 units down?

Very close, ... 3(x-4)... translation of 4 units to the RIGHT... but everything looks fine.

 

[wais]

Yes, the equation is correct. Your description of the series of transformations is also correct. The original equation can be rewritten in the form af[k(x-p)]+q as y=-2sqrt[3(x-4)]-5, which shows a vertical stretch by a factor of 2, horizontal compression by a factor of 1/3, reflection in the x-axis, horizontal translation 4 units left, and vertical translation 5 units down.