How is the graph of y=(x^2)-2 transformed to make the graph of y=√(x)-2 ?
There was another answer here before and it was correct. What happened to it? This forum is full of ghosts!
This question is making me think.
Consider y=x2 (I am only going to look at it for x>=0)
The inverse function is x=y2 which simpifies to y=sqrt(x)
Now thie inverse function is the reflection of the function in the line y=x
NOW Both the original fuction y=x2 and its inverse y=sqrt(x) have been dropped by 2 units.
So it stands to reason that the line of reflection has also been dropped by 2 units.
So the line of reflection has become y=x-2
SO If the graph y=x2-2 is reflected about the line y=x-2 it is transformed into y=sqrt(x)-2 where x>=0
There you go and the graph backs this logic up.
There was another answer here before and it was correct. What happened to it? This forum is full of ghosts!
This question is making me think.
Consider y=x2 (I am only going to look at it for x>=0)
The inverse function is x=y2 which simpifies to y=sqrt(x)
Now thie inverse function is the reflection of the function in the line y=x
NOW Both the original fuction y=x2 and its inverse y=sqrt(x) have been dropped by 2 units.
So it stands to reason that the line of reflection has also been dropped by 2 units.
So the line of reflection has become y=x-2
SO If the graph y=x2-2 is reflected about the line y=x-2 it is transformed into y=sqrt(x)-2 where x>=0
There you go and the graph backs this logic up.