For the function f(x) = #sqrtx+1/sqrtx# what are the intercepts and asymptotes ?
1 Answer
It does not intercept the
Explanation:
Given:
#f(x) = sqrt(x)+1/sqrt(x)#
Note that:

#sqrt(x)# only takes real values when#x >= 0# . 
#1/sqrt(0) = 1/0# is undefined.
So we find that
As

#sqrt(x)>0# 
#1/sqrt(x)>oo#
So
For any
As

#sqrt(x)>oo# 
#1/sqrt(x)>0#
So
By symmetry, the minimum value of
#f(1) = sqrt(1)+1/(sqrt(1)) = 1+1/1 = 2#
We now have enough information to draw the graph of
graph{(ysqrt(x)1/sqrt(x))((x1)^2+(y2)^20.01) = 0 [4.13, 15.87, 1.64, 8.36]}