Final answer:
The function g(x) has at least one y-intercept and a vertical asymptote at x = 3. Additionally, it has an oblique asymptote due to the degrees of the numerator and denominator. However, we cannot confirm an x-intercept or the domain without additional information.
Step-by-step explanation:
When analyzing the function g(x) given by the equation g(x)=(-4x*2+36)/(x-3), we can determine its key features. The function g(x) has at least one y-intercept because setting x to 0 provides a finite value for g(x), which would be g(0) = 36/(-3) = -12. This function also has a vertical asymptote at x = 3 since the denominator becomes zero and the function is undefined at that point. Additionally, g(x) will have an oblique asymptote due to the degree of the numerator being one higher than the denominator, which leads to a slant asymptote as x approaches infinity. However, we cannot determine if g(x) has at least one x-intercept without further analysis or graphing, nor can we be certain about the domain without seeing the graph of function f(x) being referred to.