Question

What are the x- and y-intercepts of `y=sqrt(2x-1)`?

Answer 1

There is no intercept with the `y` axis.

The intercept with the `x` axis is at `(1/2, 0)`

Explanation:

If `y = sqrt(2x-1)` intercepted the `y` axis, then it would be where `x=0`, but then `y = sqrt(-1)` is not defined in `RR`.

In fact, `y = sqrt(2x-1)` is only defined for `x >= 1/2`.

If `y = 0` then `2x - 1 = 0` so `x = 1/2`. So the intercept with the `x` axis is at `(1/2, 0)`

graph{sqrt(2x-1) [-10, 10, -5, 5]}