Question

g(x) = -4x^2+36 / x+3

What key features does f(x), shown in the graph, share with g(x), shown in the equation? Select three options.

at least one x-intercept
at least one y-intercept
an oblique asymptote
a vertical asymptote
the domain of x

Answer 1

g(x) = (-4x^2 + 36)/(x+3) = -4(x-3) for x ≠ -3 (the factor x+3 cancels), so g is the line y = −4x + 12 with a removable hole at x = −3.

Therefore the graph shares:
- at least one x-intercept (x = 3),
- at least one y-intercept (y = 12 at x = 0),
- the domain of x (all real numbers except x = −3, because of the hole).

It does NOT have a vertical asymptote (just a removable hole) and it does not have an oblique asymptote (the graph is exactly a line except for the hole).