Given that \((-2,3) \) is on the graph \(y = f(x)\), find a point that must be on the graph of \(y=f(2x+1)+3\). Express your answer as an ordered pair \((a,b)\) where a and b are real numbers.
I'm sorry but this doesn't seem to be the correct answer! Thanks for trying though!
Not great at this, but here's my attempt.....
y = f(2x + 1) + 3
And we can write
y = 2 ( x + 1/2) + 3
The "2" horizontally compresses the graph by a factor of 2
Thus the x coordinate of (-2,3) becomes (-2 / factor , 3) = (-2 / 2 , 3) = (-1, 3)
The "1/2" shifts the x coordinate to the left by 1/2 unit
Thus (-1,3) becomes ( -1 - 1/2 , 3) = (-3/2 , 3)
Finally....the "3" shifts this point up 3 unts ...so we have ( -3/2 , 6)
Thank you very much for putting the time and effort to solve my problem!
(It's correct by the way!)