The relation x = √(9 - y²) is compressed vertically by a factor of (1/3), then translated 1 unit to the right. Determine the equation of the transformed relation.
A. x = √(9 - 9y²) + 1
B. x = √(9 - 9y²) - 1
C. x = √[9 – (y²/9)] + 1
D. x = √[9 – (y²/9)] - 1
This one really beats me. The equation is in the form of an inverse function (unsure if this matters or not) Here is my analysis:
- Vertical compression by a factor of (1/3)
- Horizontal translation, 1 unit to the right
Translation to the right by 1 unit means x=1. Since the function is an inverse function, (A) and (C) is the likely answer since I can see that x = + 1.
Between (A) and (C), I am lost as I cannot see how a vertical compression of (1/3) factors can change the equation to (9 - 9y²) or [9 – (y²/9)].
I was thinking more like √(9 – (1/3)y²) as vertical compression is applied to y-value without taking it’s reciprocal.
Please help. Thanks.