What is the domain and range of y =sqrt(4x-1)?

Feb 13, 2016

Domain = $\left[\frac{1}{4} , \infty\right)$.

Range = $\left[0 , \infty\right)$.

Explanation:

To find the x-intercept let $y = 0$ and solve for $x$ to get $x = \frac{1}{4}$.

To find the y-intercept, let $x = 0$ to find that there is no real y-intercept.

Then draw the basic shape of the square root graph and deduce the domain (all possible allowed x-values as inputs) and the range (all possible allowed y-values as outputs).

graph{sqrt(4x-1) [-1.81, 10.68, -0.89, 5.353]}