Which equation matches the graph of the greatest integer function given below?
1 answer:
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Answer:
(a) |-9| ≠ |9| is NOT TRUE.
(b) is TRUE
(c) -7 ≤ -5 is TRUE
(d) |-1| ≥ 0 is TRUE.
Step-by-step explanation:
Solving each expression separably:
(a) |-9| ≠ |9|
By the definition of <u>MODULUS FUNCTION</u>: IxI = x, if x > 0
= (-x) if x <, 0
⇒ I-9I = -(-9) = 9, and I9I = 9
So, I-9I = I9I . Hence, |-9| ≠ |9| is NOT TRUE.
(b)
⇒
and (-8) < 3.
Hence, is TRUE
(c) -7 ≤ -5
-7 < -5 on the number line of integers.
Hence, -7 ≤ -5 is TRUE
(d) |-1| ≥ 0
I(-1)I = -(-1) = 1
and 1 > 0
Hence, |-1| ≥ 0 is TRUE.