Consider the function f(x)= (7-x)/(x+6) +2

Question

determine the domain and all intercepts?

Answer 1

The function

Simplify the function.

We know that all possible values of x  is domain of a function.

A rational function is simply fraction and in a fraction the denominator cannot be equal to 0 because it would be undefined.

To find which number make the fraction undefined create an equation where the denominator is not equal to zero.

So the domain of the function all real numbers except -6.

Domain set

To find x intercept substitute y = 0 in .

x - intercept of the function is -19.

To find y  intercept substitute x  = 0 in .

y  - intercept of the function is 3.166.