The domain will be all x such that the denominator of the fraction is not equal to zero, because division by zero is undefined. So, we need to solve:
x + 10 = 0
x = -10
The domain is all x except for x = -10.
To find the intercepts, let x = 0 and then y = 0
When x = 0, we have [(9 - 0)/(0 + 10)] + 2 = 9/10 + 2 = 29/10 One intercept is at (0, 29/10)
If y = 0, then 0 = [(9 - x)/(x + 10)] + 2
Subtracting 2 from both sides of the equation gives us:
(9 - x)/(x + 10) = -2 We can cross-multiply to solve
-2(x + 10) = 9 - x
-2x - 20 = 9 - x
-20 = 9 + x
-29 = x
The other intercept is at (-29, 0)
