College Algebra, Chapter 2, 2.3, Section 2.3, Problem 16

Determine an appropriate viewing rectangle for the equation $y = \sqrt{12x-17}$ and use it to draw the graph.

We can determine the appropriate viewing rectangle easier by getting the $x$ and $y$-intercept at the equation. So, if we set $y=0$

$\begin{equation} \begin{aligned} 0 &= \sqrt{12x-17}\\ \\ 0 &= 12x - 7 && \text{Square both sides}\\ \\ \frac{17}{12} &= x && \text{Solve for } x \end{aligned} \end{equation}$

Thus, the $x$-intercept is at $\displaystyle \left( \frac{17}{12}, 0 \right)$ or $(1.4167,0)$

Next, solving for $y$-intercept, where $x = 0$

$\begin{equation} \begin{aligned} y &= \sqrt{12(0) - 17}\\ \\ y &= \sqrt{-17} \end{aligned} \end{equation}$


The $y$-intercept does not exist.
Hence, we assume that the appropriate viewing rectangle is $[0,10]$ by $[0,10]$