
Translation
of The Principal Square Root Function 


Translation
of the principal square root function
in the direction of
the xaxis 





Translation of the principal square root function
in the direction of
the xaxis 
Horizontal
line test 
A
function f
has an inverse if no horizontal line intersects the graph of
f
more than once. 
If
any horizontal line intersects the graph of f
more than once, then f
does not have an inverse. 
A
mapping associating a unique member of the codomain with every
member of the domain of a function is called one to one
correspondence. 
A
function f
is onetoone if and only if f
has an inverse. 
Given
f
(x)
= x^{2} + y_{0}_{
}and,
since f
[f
^{}^{1}(x)]
= x 
therefore, f
[f
^{}^{1}(x)]
= [f
^{}^{1}(x)]^{2
}+ x_{0}
= x, or
[f
^{}^{1}(x)]^{2 }
= x 
x_{0}

then 



To find the
yintercept,
set x
= 0 and solve for y, that is, 




The
graph of
translated principal square root function
in the direction of
the xaxis 









Beginning
Algebra Contents B 



Copyright
© 2004  2020, Nabla Ltd. All rights reserved. 