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#1 2024-03-23 05:18:30
- nycguitarguy
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Even, Odd or Neither Functions
Determine if each function is even, odd or neither.
1. g(x) = x^3 - 27x
g(-x) = (-x)^3 - 27(-x)
g(-x) = -x^3 + 27x
I say odd.
2. f(x) = -x^3 + 12x
f(-x) = -(-x)^3 + 12(-x)
f(-x) = -(-x^3) - 12x
f(-x) = x^3 - 12x
I say neither.
3. F(x) = -x^4 + 8x^2 + 8
F(-x) = -(-x)^4 + 8(-x)^2 + 8
F(-x) = -(x^4) + 8x^2 + 8
F(-x) = -x^4 + 8x^2 + 8
I say even.
4. G(x) = -x^4 + 32x^2 + 144
G(-x) = -(-x)^4 + 32(-x)^2 + 144
G(-x) = -(x^4) + 32x^2 + 144
G(-x) = -x^4 + 32x^2 + 144
I say even.
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#2 2024-03-23 05:45:16
- Bob
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Re: Even, Odd or Neither Functions
2. f(x) = -x^3 + 12x
f(-x) = -(-x)^3 + 12(-x)
f(-x) = -(-x^3) - 12x
f(-x) = x^3 - 12x
I say neither.
This has odd powers of x so it should be an odd function.
Oh I see. f(-x) = x^3 - 12x = - (-x^3 + 12x) = - f(x)
Bob
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#3 2024-03-24 10:02:33
- nycguitarguy
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Re: Even, Odd or Neither Functions
2. f(x) = -x^3 + 12x
f(-x) = -(-x)^3 + 12(-x)
f(-x) = -(-x^3) - 12x
f(-x) = x^3 - 12x
I say neither.
This has odd powers of x so it should be an odd function.
Oh I see. f(-x) = x^3 - 12x = - (-x^3 + 12x) = - f(x)
Bob
So, am I right here? It is neither. Yes?
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
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#4 2024-03-24 14:06:15
- amnkb
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- Registered: 2023-09-19
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Re: Even, Odd or Neither Functions
Determine if each function is even, odd or neither.
With poly's its really easy: just look at the powers
1. g(x) = x^3 - 27x^1
All odd powers -> odd fcn
2. f(x) = -x^3 + 12x^1
All odd powers -> odd fcn
3. F(x) = -x^4 + 8x^2 + 8x^0
All even powers -> even fcn
4. G(x) = -x^4 + 32x^2 + 144x^0
All even powers -> even fcn
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#5 2024-03-28 09:55:32
- nycguitarguy
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Re: Even, Odd or Neither Functions
FelizNYC wrote:Determine if each function is even, odd or neither.
With poly's its really easy: just look at the powers
FelizNYC wrote:1. g(x) = x^3 - 27x^1
All odd powers -> odd fcn
FelizNYC wrote:2. f(x) = -x^3 + 12x^1
All odd powers -> odd fcn
FelizNYC wrote:3. F(x) = -x^4 + 8x^2 + 8x^0
All even powers -> even fcn
FelizNYC wrote:4. G(x) = -x^4 + 32x^2 + 144x^0
All even powers -> even fcn
Ok. Good outline of information.
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
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