Question

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases what happens

Answer 1

then f(x) is liner function.

Answer 2

See i drew a cubic function which has the same property as stated above

Answer 3

Its usually a polynomial that is odd .. meaning it has symmetry around its origin and -f(x)=f(-x)

Answer 4

Also the function must me be positive such as y=x Not y=-x
So illustrate this for you

Answer 5

y=x --> positive function
As you see as x increases then f(x) increases
as x decreases then f(x) decreases

Answer 6

y=-x --> negative function
As x increases y decreases
and as x decreases then y increases

Answer 7

SO basically it needs to be a positive function and odd

Answer 8

Not necessarily odd. \(x^3+3\) will still be a function satisfying the requirements.

Answer 9

Thats true
so in that case we can just tweak it a bit
and say the degree of the polynomial must be