7
QuizMultiple Choice

Domain and Range — Quiz

Question 7 • Mathematics III

When graphing the function f of x is equal to the fraction with numerator x squared minus 81 and denominator x squared minus 11 x plus 18 on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?

Answer
A
Xmin: minus 10 , Xmax: 0 Ymin: minus 10 , Ymax: 0
B
Xmin: minus 10 , Xmax: 10 Ymin: minus 10 , Ymax: 10
C
Xmin: minus 5 , Xmax: 5 Ymin: minus 5 , Ymax: 5
D
Xmin: 0 , Xmax: 10 Ymin: 0 , Ymax: 10

Explanation

The denominator factors as (x − 9)(x − 2), so the graph has a vertical asymptote at x = 2 and a hole at x = 9. A window from −10 to 10 on the x-axis includes both features and shows the graph on either side of them; the same broad range on the y-axis helps display its behavior. The other windows either omit negative x-values or do not extend far enough to show the hole at x = 9.

AI-written and checked against the verified answer.

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