# Thread: Increasing and Decreasing function

1. ## Increasing and Decreasing function

I have been searching the definition for increasing and decreasing functions.

Most of the definition define f such that f : A -> R where A is a subset of real numbers R. Then f is increasing if f(y)>f(x) where y>x and x, y in A.

Is it necessary that the domain of f must be a subset of R?

Can the domain be R?

Thanks for those who help...

2. if your y value is increasing as your x value is increasing, the function is increasing.

for example f(x) = x

if x = 0, y = 0
if x = 1, y = 1

So as you go from left to right, your y value gets higher, thus it is increasing.
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I've attached some graphs of increasing functions.

(I feel like a kid with candy)

edit: Note that $\displaystyle f(x)=x^{3}$ is not increasing at the point (0,0), but it is increasing everywhere else.

3. And here are some examples of decreasing functions, a decreasing function has the y value get lower as x increases.

So as x goes from left to right, the value of f(x) goes down.

Again, note that $\displaystyle f(x)=-(x-5)^{3}$ is not decreasing at the point (0,0)