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how is the graph of y=(x^2)-2 transformed to make the graph of y=√(x)-2

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How is the graph of y=(x^2)-2 transformed to make the graph of y=√(x)-2 ?

Guest Jun 24, 2014

Best Answer

#1
+94110
+10

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.

Melody  Jun 25, 2014
#1
+94110
+10
Best Answer

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.

Melody  Jun 25, 2014
#2
+92744
0

Nice answer and graph, Melody......jboy314 had an answer yesterday, if I remember correctly....ghosts, indeed!!!

CPhill  Jun 25, 2014
#3
+94110
0

Yes I liked this question.  I don't remember seeing one like it before. (thanks for the thumbs up)

Melody  Jun 25, 2014

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