Practice Test

Question 8 • Algebra II

Which graph shows the solution set of the fraction with numerator x squared plus 9 x plus 20 and denominator x squared minus x minus 20 is greater than or equal to 0 ?

Answer

Image with description A number line from negative 5 to 6. An open circle is at negative 4 with a ray pointing left. An open circle is at 5 with a ray pointing right.

Image with description A number line from negative 5 to 6. A segment connects a closed circle at negative 5 to an open circle at negative 4. A segment connects an open circle at negative 4 to an open circle at 5.

Image with description A number line from negative 5 to 6. An open circle is at negative 5 with a ray pointing left. An open circle is at 5 with a ray pointing right.

Image with description A number line with a horizontal axis labeled x with tick marks from negative 5 to 6. A line starts at a solid circle at negative 5 and extends to the left with an arrowhead. Another line starts at an open circle at 5 and extends to the right with an arrowhead.

Explanation

Factor the numerator and denominator: (x + 5)(x + 4) / [(x - 5)(x + 4)]. The expression is undefined at x = -4 and x = 5, and after canceling the common factor its sign matches (x + 5)/(x - 5). This is nonnegative for x ≤ -5 or x > 5; -5 is included because it makes the numerator zero, while 5 is excluded because it makes the denominator zero. Thus the graph has a closed circle at -5 with a ray left and an open circle at 5 with a ray right: choice D.

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