How do I identify the functions domain and range of f(x)=1/x-5 ?

Question

I need this to be explained as simple as possible because I am completely lost.

Answer 1

This question was discussed in a previous post

Answer 2

Hello Jay

 

The domain of a function is all possible inputs, or all possible values which x could be.  For your particular function, instead of asking yourself "what could x be," it might be easier to ask "what can't x be?" In the function, (x - 5) is in the denominator, therefore, the quantity (x - 5) cannot be equal to zero since you are not allowed to divide by zero (this will produce an undefined output).  In order to determine the domain, simply set the denominator equal to zero to determine what x can't be.

 

x - 5 ≠ 0
     x ≠ 5

 

Solving for x produces -5. Therefore, x cannot be equal to -5 since this will produce a value of zero for the denominator. 

 

You could also write the domain as ...

 

D: x = all real numbers, but not 5

 

The range of the function is all possible outputs, or "y" values, as one considers all possible inputs (a.k.a. the domain).  A good way to check the range is to graph the function in a graphing calculator. Check out the graph. The range of the function will be the "area" between the highest and lowest point of the graph. In this case the graph extends from negative infinity to positive infinity, but does not have an output for y = 0.  Since the outputs of the function cover all possible values for y, with the exception of 0, the range is...

 

y = all real numbers, but not 0

Answer 3

Hi Jay,

Here is a simple explanation.

Let's begin with the domain. Think of the domain as all possible input values for x. In other words, what x values can and can't we plug into this formula. In this situation, there is one value of x that we cannot plug into this formula. The domain of this function will include all values of x from negative infinity to infinity, excluding the one value that will cause the denominator (x-5) to be equal to zero.

 

Accordingly, the range is all of the possible output values for f(x). Are there values that this function will never produce? The range will be all numbers excluding those values. In this case, we know that f(x) will never be equal to zero, as the denominator cannot be equal to zero and 1=/=0.

 

This question can also be approached by looking at a graph of the function, and seeing what x and y (f(x)) values are valid for the graph.