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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (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:
c%28y+-+k%29+=+sqrt%28b%28x+-+h%29%29
Substituting your values for the parameters:
-1%28y+-+%28-5%29%29+=+sqrt%28%281%2F3%29%28x+-+%28-2%29%29%29
Now all that is left is to simplify and solve for y:
-1%28y+%2B+5%29+=+sqrt%28%281%2F3%29%28x+%2B+2%29%29
Rationalize the denominator in the square root:
-1%28y+%2B+5%29+=+sqrt%28%283%2F9%29%28x+%2B+2%29%29
-1%28y+%2B+5%29+=+sqrt%28%283%29%28x+%2B+2%29%29%2Fsqrt%289%29
-1%28y+%2B+5%29+=+sqrt%283x+%2B+6%29%2F3
Multiply both sides by -1:
y+%2B+5+=+-+sqrt%283x+%2B+6%29%2F3
Subtract 5 from both sides:
y+=+-5+-+sqrt%283x+%2B+6%29%2F3