Question

Consider the function f(x)=(8-x)/(x+9)+2 Algebraically determine the domain and all of the intercepts.

Answer 1

f(x) = (8 - x)/(x + 9) + 2
The domain is all real numbers except -9.

The x-intercepts are the values of x for which y = 0.
0 = 8 - x + 2(x + 9) = 8 - x + 2x + 18 = x + 26
x = -26

The y-intercepts are the values of f(x) for which x = 0
f(x) = 8/9 + 2 = 2 8/9