To solve for f, you need to isolate/get the variable by itself in the equation:
4(0.5f - 0.25) = 6 + f       Distribute 4 into (0.5f - 0.25)
(4)0.5f + (4)(-0.25) = 6 + f
2f - 1 = 6 + f        Subtract f on both sides to get "f" on one side of the equation
2f - f - 1 = 6 + f - f
f - 1 = 6       Add 1 on both sides to get "f" by itself
f - 1 + 1 = 6 + 1
f = 7
PROOF
4(0.5f - 0.25) = 6 + f      Substitute/plug in 7 into "f" since f = 7
4(0.5(7) - 0.25) = 6 + 7
4(3.5 - 0.25) = 13
4(3.25) = 13
13 = 13
 
        
             
        
        
        
Given the function:

The function can also be written as:

The range of the function will be all set of y values. 
To find the range, let's graph the function below.
We have:
From the graph above, all possibe y values range from 0 to infinity.
Therefore, the range of the function is from zero infinity.
In interval notation:
Range = (0, +∞)
ANSWER:
4. (0, +∞)
 
        
             
        
        
        
Answer: The slope is  .
.
Step-by-step explanation:
1. You set up your Slope Formula  .
.
2. Substitue your points into the formula. .
. 
3. Once you substitute, you will solve the equation .
.
4. Simplify the equation if you have to  .
.
 
        
             
        
        
        
I cannot suggest anything other than the set of real numbers here, but maybe someone else can provide a better answer. As long as you increase or decrease x (which is a real number) then you will get a real number, or the infinite set of real numbers.