Answer
The given relation defines $y$ as a function of $x$.
domain: $[-\frac{1}{4}, \infty)$
range: $[0, +\infty)$
Work Step by Step
The given equation above will give only one value of $y$ for every value of $x$. This means that each $x$ is paired with only one value of $y$.
Thus, the given relation defines $y$ as a function of $x$.
Note that in $\sqrt{4x+1}$, the value of the radicand (which in this case is $4x+2$) cannot be negative.
Thus,
$4x+1 \ge 0
\\4x \ge -1
\\x \ge \frac{-1}{4}$
This means that the value of $x$ can be any number greater than or equal to $-\frac{1}{4}$. Thus, the domain is $[-\frac{1}{4}, \infty)$.
Note that $\sqrt{4x+1}$ represents the principal square root of $4x+1$. The principal square root of a number is either zero or positive.
Thus, the value of $y$ can be any real number greater than or equal to zero. In interval notation, the range is $[0, +\infty)$.
