Hello! I am a little confused about graph transformations and I have some questions that I don't really know how to solve...Please help! Thank you!
1)
The transformations A,B and C are as follows:
A: A translation of 1 unit in the negative y direction
B: A stretching parallel to the y-axis (with x-axis invariant) with a scale factor of 2
C: A reflection about the x-axis
A curve undergoes in succession, the above transformations A,B and C and the equation of the resulting curve is y = -2(x^2) -6. Determine the equation of the curve before the transformations were effected. [Is it possible to view the equation of the resulting curve as y= -2 (x^2 -3)? But I think this will give a different original equation from if I use the given resulting equation??]
2)
The equation of a graph is y = (ax)/(bx-y), and y= c is the horizontal asymptote while x = d is the vertical asymtote of this graph. Given that c = d = 1/2, what are the values of a and b? [If I am not wrong, b should be 2, but I don't know how to find a....Is a = 1?]
3)
Consider the curve (5x + 10)^2 - (y-3)^2 = 25. Prove, using an algebraic method, that x cannot lie between two certain values (which are to be determined). [I know how the given equation can be expressed to become the standard equation of a hyperbola, but I am not sure what is the "algebraic method" the question is asking for...]
Thank you very very much for helping me!