Answer
The given relation defines $y$ as a function of $x$.
domain: $(-\infty, 3.5]$
range: $[0, +\infty)$
Work Step by Step
The given equation above will give only one value of $y$ for every value of $x$ within its domain. 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 $\sqrt{7-2x}$, the value of the radicand (which in this case is $7-2x$) cannot be negative.
Thus,
$7-2x \ge 0
\\-2x \ge -7
\\\frac{-2x}{-2} \le \frac{-7}{-2}
\\x \le 3.5$
This means that the value of $x$ can be any number less than or equal to $3.5$. Thus, the domain is $(-\infty, 3.5]$.
Note that $\sqrt{7-2x}$ represents the principal square root of $7-2x$. 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 $[0, +\infty)$.
