Question

Which quadrants and axes does `f(x)=x^3-sqrtx` pass through?

Answer 1

Passes through the origin. As `x >=0` for `sqrt x` to be real, the graph prevails in the 1st and 4th quadrants only. It makes an intercept 1 on the x-axis, at (1, 0).

Explanation:

For x in (0, 1), we get the bottom point at `((1/6)^(2/5), -0.21)`, in the 4th quadrant. In the first quadrant, as `x to oo, f(x) to oo`...