SOLUTION: Can you help me solve this question: 1. Write an equation for the graph of y=sqrtx, that has been horizontally expanded by a factor of 3, reflected across the x-axis, translated 2

Question 204354: Can you help me solve this question: 1. Write an equation for the graph of y=sqrtx, that has been horizontally expanded by a factor of 3, reflected across the x-axis, translated 2 units to the left, and down 5 units.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
In general, if you have a function (let's call it y = f(x)), then the graph of
c(y - k) = f(b(x - h)) will be

Shifted/translated right by "h" units
Shifted/translated up by "k" units
Compressed horizontally by a factor of "b"
Be reflected in the y-axis if b < 0
Be compressed vertically by a factor of "c"
Be reflected in the x-axis if c < 0

Since you want

a translation left of 2, your "h" will be -2.
a translation down of 5, your "k" will be -5.
a horizontal expansion factor of 3 (but no horizontal reflexion), your "b" will be 1/3.
no vertical compression/expansion but you do want a vertical reflexion, you "c" will be -1.

Applying the general form to your function:

Substituting your values for the parameters:

Now all that is left is to simplify and solve for y:

Rationalize the denominator in the square root:

Multiply both sides by -1:

Subtract 5 from both sides:

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