how to check a function with multiple variables in a visual way

Question

I am not very math inclined, so sorry in advanced if the terminology is not correct.

I have a system of variables; imagine an array of sensors, which return temperature, pressure, humidity, for sake of simplicity. I would like to calculate a coefficient between 1 and 100, based on these values; I know the min and max of each of these variables; so I shall get something like this:

randomnumber between 1 and 100
temperature between 10 and 60
pressure between 1 and 15
humidity between 1 and 100

RandomNumber + ((temperature - humidity - pressure)/3) = 100

Now if I want to verify that in fact I get numbers between 1 and 100 from that function, is there an "automated" way to do so?

I could write some code in python, that create random values in my set ranges and run that function; but I believe there are better ways.

How do you actually verify functions with multiple values, without writing code in some language, that will solve multiple times the function? I saw some plotting utility online, but they usually deal with funcitons that have one or at most 2 variables.

Answer 1

To determine the minimum and maximum values of your function: $RandomNumber+((temperature−humidity−pressure)/3)$ you need to consider how each variable affects the total. This is slightly clearer if you rewrite the function to highlight how each term works.

$$RandomNumber+\frac{temperature}{3}-\frac{humidity}{3}-\frac{pressure}{3}$$

Looking at this we can see that:

• Increasing $RandomNumber$ will increase the total.

• Increasing $temperature$ will increase the total.

*Increasing $humidity$ will decrease the total.

*Increasing $pressure$ will decrease the total.

So to minimize the total you want to minimize $RandomNumber$ and $temperature$ and maximize $humidity$ and $pressure$. So the total would be: $1+\frac{10-100-15}{3}=1+\frac{-105}{3}=-34$.

And to maximize the total you want to maximize $RandomNumber$ and $temperature$ and minimize $humdity$ and $pressure$. So the total would be: $100+\frac{60-1-1}=100+\frac{58}{3}=117\frac{1}{3}$.

So your values are in the range $-34$ to $117\frac{1}{3}$.