f(x) = (x+2)/(x-6)

what is the domain of f?

How would I find this? without graphing

domain is simply the possible x's you could use.

Remember we cannot divide by zero, so the only thing we have to worry about is the denominator.

when is x-6 = 0 ?
in your head you should be able to see that it cannot be 6

domain: any real number, x ≠ 6

ok, thanks

To find the domain of a function, we need to determine the set of all possible input values (x-values) for which the function is defined. In this case, we have the function f(x) = (x + 2)/(x - 6).

To find the domain, we need to consider any values of x that may cause division by zero or results in undefined behavior. In this function, the only potential issue is division by zero, since dividing by zero is undefined.

To identify the x-values that may result in division by zero, we set the denominator equal to zero and solve for x:

x - 6 = 0

Adding 6 to both sides, we get:

x = 6

Therefore, x = 6 is the x-value that makes the denominator zero. So the function is not defined at x = 6.

Hence, the domain of f(x) is all real numbers except x = 6. In interval notation, we can write the domain as (-∞, 6) U (6, ∞). This means that any real number except 6 can be an input for this function.