Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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?

amnkb

Member

Registered: 2023-09-19

Posts: 253

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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

Ok. Good outline of information.