Teaching Notes 4.3: Graphing Disjunctions
Disjunctions with one variable can be graphed on a number line. Some students mistakenly
believe that, like conjunctions, disjunctions may also be rewritten as one inequality.- Explain that a disjunction is a sentence formed by joining two sentences with the word ‘‘or.’’
Note that if at least one of the statements is true, then the disjunction is true. A disjunction
cannot be rewritten as one combined inequality. - Explain that graphing a disjunction is similar to graphing an inequality, except that two
inequalities are graphed on the same number line. - Review the information and example graphs on the worksheet with your students. Note that
a closed circle shows that the number paired with the point is included on the graph. An open
circle shows that the number paired with the point is not included on the graph.
EXTRA HELP:
The shadings on the graph of a disjunction point in opposite directions. One part of the graph is
shaded to the right and the other part is shaded to the left.ANSWER KEY:
Note:The number lines are not drawn to scale.
(1)
13(2)
05
(3)
− 11
(4)
12
(5)
− 13
(6)
710
(7)
03
(8)
12
(9)
− 2 − 1
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(Challenge)The graph of a disjunction would model the situation. There would be an empty circle
on the number line at 5 and 10. The number line would be shaded to the right of 10 and to the
left of 5.
------------------------------------------------------------------------------------------142 THE ALGEBRA TEACHER’S GUIDE