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Chapter 1: Problem 26

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$y=\sqrt{2 x-1}$$

Short Answer

Expert verified
The x-intercept is at \(x = 0.5\), and there is no y-intercept for the equation \(y=\sqrt{2x-1}\).

Step by step solution

01

Solve for the x-intercept

To find the x-intercept, substitute \(y = 0\) into the equation and solve for \(x\). It gives us \[0 = \sqrt{2x - 1}\] Squaring both sides of the equation to eliminate the square root, we obtain \(0 = 2x - 1\). Solving this equation gives \(x = 0.5\). So, the x-intercept is at \(x = 0.5\).
02

Solve the y-intercept

To find the y-intercept, set \(x = 0\) in the equation. We have \(y = \sqrt{2*0 - 1}\). The square root of a negative number doesn't exist in the real number system. So there is no y-intercept in this case.

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