Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = \left| x ^ { 2 } - 7 \right|$$
A) $[ - 10,10 ]$ by $[ - 15,15 ]$
B) $[ - 5,5 ]$ by $[ - 2,10 ]$
C) $[ - 5,5 ]$ by $[ - 15,15 ]$
D) $[ 0,5 ]$ by $[ - 2,10 ]$

Question

Quizplus · Accepted Answer

The function $f(x) = |x^2 - 7|$ has a vertex at the point where $x^2 = 7$, which is approximately at $x = \pm \sqrt{7}$ or approximately $x = \pm 2.65$. This means the most interesting features of the graph, including the vertex and the parts where the function changes from increasing to decreasing or vice versa, will be visible within the range of $[-5, 5]$ for $x$. The range of $[-2, 10]$ for $y$ is appropriate because the minimum value of $|x^2 - 7|$ is 0 (when $x^2 = 7$), and the maximum value within the given $x$ range will not exceed 10. This makes option B the most suitable viewing window to capture the essential features of the graph.

Use a Graphing Calculator or Computer to Determine Which of the Given