am i right?
domain:
range;?
how can i graph this?
thanks.
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domain:
Not exactly
This will give real values if
x^2 + 2 > 0
Since Square of every real number is >0
And +2 will not make it negative
Hence its true for all real x
------------------------------------------------
Range:
Thus
x^2 = y^2 - 2
For rage you need to find all y that satisfy above values
thus
So all y EXCEPT ( -2,2)
But y should be negative because of the question's negative sign
so range is
[2,infinity)
------------------------------------
Graph:
Note that y will always be negative
y^2 = x^2 + 2
y^2 -x^2 = 2
This is a 90degree rotated hyperbola (Vertical hyperbola)
the upper part of vertical hyperbola should not be drawn
The graph below is for
Again Don't draw the upper leaf of this type of hyperbola
ok I understand this part. thanks
I didn't understand the range can you explain further? thanks so muchRange:
how did you get x^2 = y^2 - 2
Thus
x^2 = y^2 - 2
For range you need to find all y that satisfy above values
thus
So all y EXCEPT ( -2,2)
But y should be negative because of the question's negative sign
so range is
[2,infinity)
First of all there was a TYPO at the last step, corrected here (written y as negative and gave you +ve range)
Now
add (-2) on both sides
y^2 - 2 = x^2
And
Now this represents x in terms of y
Domain of x is R
what are the values that y can take to give all x in R
This is done by finding all the values in this function
in other words we find the domain(meaning all values that y can take) of this function
Hence I followed the steps below
-----------------------------------------------------
thus
So all y EXCEPT ( -2,2)
-----------------------------------------------------
But y should be negative because of the question's negative sign
this happens because
has LHS negative (-1 x square root= negative number)
so range is
(-infinity,-2]