Page 113 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

testing with x = 3
2(x – 3) + 3x = 2(3 – 3) + 3(3) =0+9
=9
5(x – 2) + 2 = 5(3 – 2) + 2 =5+2
=7
These expressions are not equivalent because the same input gives different outputs. o use a table of values to test the output for various inputs:
▪ compare x(x – 4) and x2 – 4x using a table of values:
x
x(x – 4)
x2 – 4x
0
0(0 − 4) =0
02 − 4(0) =0
1
1(1 − 4) = 1(−3)
= −3
12 − 4(1) =1−4
= −3
5
5(5 − 4) = 5(1)
=5
52 − 4(5) = 25 − 20 =5
10
10(10 − 4) = 10(6)
= 60
102 − 4(10) = 100 − 40
= 60
1 2
1 (1 − 4) 22
= 1 (− 7) 22
=−7 4
(1)2 − 4 (1) 22
=1−2 4
=−7 4
−2
−2(−2 − 4) = −2(−6)
= 12
(−2)2 − 4(−2) =4+8
= 12
−3
−3(−3 − 4) = −3(−7)
= 21
(−3)2 − 4(−3) = 9 + 12
= 21
Although these expressions are equivalent for the tested inputs, it is impossible to determine for certain whether they are always equivalent without using another method.
• comparing using graphical methods:
o graph the expressions to determine whether the graphs are identical:
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