What function is neither increasing nor decreasing?

Constant function
Constant function: When a function is neither increasing nor decreasing in the given interval, then such type of function is known as constant function. Or in other words, when a function, f(x), is constant, the value of f(x) does not change as x increases.

How do you prove that a function is one-to-one increasing?

If some horizontal line intersects the graph of the function more than once, then the function is not one-to-one. If no horizontal line intersects the graph of the function more than once, then the function is one-to-one. ∀x1, ∀x2, x1 = x2 implies f(x1) = f(x2).

Is a one to one function always increasing?

If a function is continuous and one – to – one then it is either always increasing or always decreasing. An easy way to see this on a graph is to draw a horizontal line through the graph . If the line only cuts the curve once then the function is one – to – one.

How do you know if a function is increasing decreasing or neither?

If we have a function of time, we might discuss when a function is increasing or decreasing, and we are talking about for which t-values is a function increasing or decreasing. If f′(x)>0 on an open interval, then f is increasing on the interval. If f′(x)<0 on an open interval, then f is decreasing on the interval.

How do you write a function that is increasing?

A function is increasing on some interval of its domain if f(a) > f(b) for all a, b in that interval such that a > b. A function is decreasing on some interval of its domain if f(a) < f(b) for all a, b in that interval such that a > b. More casually put: a function is increasing if the graph rises to the right.

What is a function that is one to one but not onto?

Put y=1. x=12=0.5, which cannot be true as x∈N as supposed in solution. Hence, the given function is not onto. So, f(x)=2x is an example of One-one but not onto function.