Math Is Fun Forum

criticalCat

Novice

Registered: 2025-09-01

Posts: 9

Is it possible to write a formula for this graph?

I have the following graph:

I'm wondering if it is possible to describe the graph using a mathematical formula?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,811

Re: Is it possible to write a formula for this graph?

hi criticalCat

Weclome to the forum.

As the graph has three entirely different sections, it won't be possible to find a single formula for this. The usual way to describe a graph like this is by a piecewise definition.

ie. Find separate formulas for each section.

The first would be:

For x ≤ -4  f(x) = 3x + 25

Are you able to find the correct formulas for the other two sections?

Please post back.

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

criticalCat

Novice

Registered: 2025-09-01

Posts: 9

Re: Is it possible to write a formula for this graph?

I think the formulas for the next two sections would be :

Is it possible to get x from f(x) using partial functions?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,811

Re: Is it possible to write a formula for this graph?

hi criticalCat

Both answers correct.

The first and last functions are invertable, so you could construct a similar function definition for 
x in terms of f(x).  The middle has no inverse because many values of x lead to the same f(x); so there is no one formula that gives x when you know 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