What does this have to do with trigonometry?

(x^2 + 2)/(x + 4) = 1/2

x^2 + 2 = (x + 4)/2

2x^2 - x = 0

x(2x - 1) = 0

x = 0 or x = 1/2

The domain is x>-4, x<-4

f(x) = 0 when x^2 + 2 = 0

No real roots, so f does not intercept x axis.

f(0) = 2/4 = 1/2

y intercept at y = 1/2