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Which of the following can be a correct piece-wise definition of the f
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28 Feb 2022, 07:15
28 Feb 2022, 07:15
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Which of the following can be a correct piece-wise definition of the function \(h(x) = |x + 2|\)?
(A) h(x) = x + 2 when x ≥ 0 and x - 2 when x < 0
(B) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 2
(C) h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
(D) h(x) = x + 2 when x ≥ -2 and x - 2 when x < 2
(E) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 0
(A) h(x) = x + 2 when x ≥ 0 and x - 2 when x < 0
(B) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 2
(C) h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
(D) h(x) = x + 2 when x ≥ -2 and x - 2 when x < 2
(E) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 0
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Re: Which of the following can be a correct piece-wise definition of the f
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06 Mar 2022, 21:17
06 Mar 2022, 21:17
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Carcass wrote:
Which of the following can be a correct piece-wise definition of the function \(h(x) = |x + 2|\)?
(A) h(x) = x + 2 when x ≥ 0 and x - 2 when x < 0
(B) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 2
(C) h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
(D) h(x) = x + 2 when x ≥ -2 and x - 2 when x < 2
(E) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 0
(A) h(x) = x + 2 when x ≥ 0 and x - 2 when x < 0
(B) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 2
(C) h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
(D) h(x) = x + 2 when x ≥ -2 and x - 2 when x < 2
(E) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 0
Try to draw the graph of the given function with some ordered pairs
\(h(x) = |x + 2|\)
x = -7, h(x) = 5
x = -6, h(x) = 4
x = -5, h(x) = 3
x = -4, h(x) = 2
x = -3, h(x) = 1
x = -2, h(x) = 0
x = -1, h(x) = 1
x = 0, h(x) = 2
x = 1, h(x) = 3
x = 2, h(x) = 4
x = 3, h(x) = 5
Let us check the option choices;
(A) h(x) = x + 2 when x ≥ 0 and x - 2 when x < 0
if we plug x = -1, h(x) must be -3
But we clearly see h(x) = 1
(B) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 2
if we plug x = 1, h(x) must be 1
But we clearly see h(x) = 3
(C) h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
if we plug x = -3, h(x) must be 1
we clearly see h(x) = 1
Check 1 or 2 more values (distant)
if we plug x = -5, h(x) must be 3
we clearly see h(x) = 3
(D) h(x) = x + 2 when x ≥ -2 and x - 2 when x < 2
if we plug x = 1, h(x) must be -1
But we clearly see h(x) = 3
(E) h(x) = x + 2 when x ≥ 2 and -x + 2 when x < 0
if we plug x = -1, h(x) must be 3
But we clearly see h(x) = 1
Hence, option C
General Discussion
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Which of the following can be a correct piece-wise definition of the f
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07 Aug 2022, 10:39
07 Aug 2022, 10:39
Theory:
Given that \(h(x) = |x + 2|\) and we need to simplify the function
=> h(x) = |x+2| = x+2 when x + 2 ≥ 0 or x ≥ - 2
and h(x) = -(x+2) when x + 2 < 0 or x < -2
=> h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
- ➡ |Y| = Y for Y ≥ 0 and
➡ |Y| = -Y for Y < 0
Given that \(h(x) = |x + 2|\) and we need to simplify the function
=> h(x) = |x+2| = x+2 when x + 2 ≥ 0 or x ≥ - 2
and h(x) = -(x+2) when x + 2 < 0 or x < -2
=> h(x) = x + 2 when x ≥ -2 and -x - 2 when x < -2
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
