SOLUTION: I apologize if this is the wrong section. I just recently got back into school and taking a math course currently and I just got stuck on a question. These type of problems is wher

Algebra ->  Graphs -> SOLUTION: I apologize if this is the wrong section. I just recently got back into school and taking a math course currently and I just got stuck on a question. These type of problems is wher      Log On


   

Question 588893: I apologize if this is the wrong section. I just recently got back into school and taking a math course currently and I just got stuck on a question. These type of problems is where I get confused about.
The problem is:
Find the range of y=f(x) and graph it.

f(x){-1/4(x) if x cannot = to 0; -6 if x=0}


I appreciate it as this will help me with the next few problems.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The domain of a function is the set of possible values for x.
For example the domain for f%28x%29=sqrt%28x%29 is all the non-negative x values.
We may state it as {x: x%3E=0 }
The range is the set of all the possible y=f(x) values
For example the range for f%28x%29=x%5E2%2B2 is {y: y%3E=2 } because all the values for y=f(x) will be 2 or greater.

f(x)=1/(4x)= 1%2F%284x%29 has a domain of all real numbers except x=0, because when the denominator is zero, the function is undefined; f(0) does not exist.
The function can be "patched up" by defining f(0)=-6, or some such thing.
The range of that function is all real numbers except y=0 because there is no value for x that maxes f(x)=0. We could fix it by defining f(0)=0, and then the domain and the range would be all real numbers.
The graph of f(x)=1/(4x) is
graph%28300%2C300%2C+-3%2C3%2C-10%2C10%2C1%2F%284x%29%29 If there is a definition "patch-up" for x=0, there is an extra point on the y axis. If not patched up, the function never touches the y axis.