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

Jun 16, 2015

There is no intercept with the $y$ axis.

The intercept with the $x$ axis is at $\left(\frac{1}{2} , 0\right)$

#### Explanation:

If $y = \sqrt{2 x - 1}$ intercepted the $y$ axis, then it would be where $x = 0$, but then $y = \sqrt{- 1}$ is not defined in $\mathbb{R}$.

In fact, $y = \sqrt{2 x - 1}$ is only defined for $x \ge \frac{1}{2}$.

If $y = 0$ then $2 x - 1 = 0$ so $x = \frac{1}{2}$. So the intercept with the $x$ axis is at $\left(\frac{1}{2} , 0\right)$

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