Question

Which quadrants and axes does `f(x)=sin(sqrtx)` pass through?

Answer 1

First and fourth quadrant

Explanation:

The function is only valid for `x in RR^+`, as the root of a negative is complex, so hence quadrants 2 and 3 can be disregarded.

Hence the function will pass through Quadrans 1 and 4, for example `sin root2 ((pi/2)^2 )` evidently lies in the first quadrant, and `sin root2 (((3pi)/2)^2)` evidenlty lies in the lies in the fourth quadrant.

Passing through the positive x axis.

graph{y=sin(x^(1/2)) [-9.84, 30.16, -10.4, 9.6]}