Teaching Notes 4.2: Graphing Conjunctions
Graphing conjunctions is a skill that requires students to interpret inequalities and graph them
according to their interpretations. Incorrectinterpretations lead to faulty graphs.- Explain to your students that a conjunction is a sentence formed by joining two sentences
with the word ‘‘and.’’ Two inequalities can be joined by ‘‘and’’ to form a conjunction. - Explain that all conjunctions with one variable can be graphed on a number line. Depending
on the abilities of your students, you may find it helpful to present a simple number line and
review its properties. Note that a conjunction is true when both sentences are true. - Review the information and example graphs on the worksheet with your students. Substitute
thenumbers−1foraand3forbanddiscusseachgraph.Forexample− 1 ≤x≤3containsthe
numbers−1 and 3 and all of the numbers between them. Remind your students that this
includes decimals and fractions. Also note that the graph has closed circles. This means that
the number paired with the point is included on the graph. Contrast this to the fourth graph,
a<x <b. An open circle means that the number paired with the point is not included on
the graph. - Review rewriting two inequalities as one. For example,x>0and1≥xcan be written as
0 <xandx≤1, which is the same as 0<x≤1.
EXTRA HELP:
Writing a conjunction as one combined conjunction is easier to graph.ANSWER KEY:
Note:The number lines are not drawn to scale.
(1)
05(2)
25
(3)
− 30
(4)
− 5 − 4
(5)
34
(6)
− 12
(7)
− 11
(8)
03
(9)
− 20
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(Challenge)− 3 ≤x<1.
------------------------------------------------------------------------------------------140 THE ALGEBRA TEACHER’S GUIDE