How can I convert a value in the range of 0 to1 into a value of -1 to 1

Question

Okay so I am programming a video game. I am using a what's called a slider that can be dragged across the screen with the mouse that will give a value based off it's position. If it is dragged all the way to the left, the value it returns is 0. If it is dragged all the way to the right, the value it returns is 1, and then obviously if it it's in the middle it will return the value of 0.5. What I need to do is be able to get the slider value to return as -1 if it is all the way to the left, +1 if it is all the way to the right, and 0 if it's in the middle. I've tried messing around with adding and multiplying but I can't get it to work. I'm honestly pretty bad at math and if someone could walk me through the equation step by step that would help me a lot. Any info to help me solve this is appreciated :)

Answer 1

You can try fitting a linear function.

 

f(x) = ax + b

 

f(0) = -1

f(1) = 1

 

Now solve for a and b.

 

f(0) = -1 

-1 = a(0) + b ⇒

b = -1

 

f(1) = 1

a(1) + b = 1

a -1 = 1

a = 2

 

f(x) = 2x -1