For each statement below, determine whether it is a) always true b) sometimes tr
ID: 3168536 • Letter: F
Question
For each statement below, determine whether it is a) always true b) sometimes true or c) never true. 1) Test each statement for these three numbers: x 0, x2 2) Draw your conclusion. An example is provided. , and x4 substitute x-21Substitutexto-4-Conclusion 2) +2>0 2 +2>0 4> 0 TRUE Substitute x-o Statement Note: The absote 0 +0>0 ahways positive 4+-40 Sometimes true 4+4>0 0>0 0>0 False False Note: The absohute abways positive. c) x x -3 UNDEFINED r3 Zero may not be in the denominatorExplanation / Answer
a) x > -x
substitute x = 0
0 > -0
false
substitute x = 2
2 > -2
true
substitute x = -4
-4 > -(-4)
false
conclusion : sometimes true
b) |x | > x
substitute x = 0
|0| > 0
false
substitute x = 2
|2| > 2
false
substitute x = -4
|-4| > -4
true
conclusion : sometimes true
c) x^2 < 0
substitute x = 0
0 < 0
false
substitute x= 2
2^2 < 0
false
substitute x = -4
(-4)^2 < 0
16 <0
false
conclusion : never true
d) x^2 > x
substitute x = 0
0^2 > 0
false
substitute x = 2
2^2 > 2
true
substitute x = -4
(-4)^2 > -4
16 > -4
true
conclusion : sometimes true
e) x^-3 = 1/x^3
substitute x = 0
0^-3 = 1/ 0^3
undefined
substitute x = 2
2^-3 = 1/ 2^3
true
substitute x = -4
-4^-3 = 1/ -4^3
true
conclusion : sometimes true
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.