+895 For these questions, find the domain and determine if there are any vertical asymptote(s) and/or holes.
a) \(g(x)=\frac{4x^2+6}{x+1}\)
b) \(h(x)=\frac{5x^2+2}{x^2-9}\)
+128474 g(x) = [ 4x^2 + 6 ] / [ x + 1]
Domain = all reals except for x = -1 [ this makes the denominator = 0 ]
There will be something known as a "slant" asymptote and a vertical asymptote at x = -1
See the graph, here : https://www.desmos.com/calculator/orq4zkm2xz
h(x) = [ 5x^2 + 2] / [ x^2 - 9 ]
Domain = all reals except x = -3 and x = 3 [ these make the denominator = 0 ]
Vertical asymptotes will occur at x = - 3 and x =3
See the graph, here : https://www.desmos.com/calculator/6flwyghtuw
