Help me with some algebra 2 ! I'm suffering from summer learning loss :(

Question

steve816 · Answer

Given $$f(x)=\frac{ x^2+7x+12 }{ x^2-16 }$$ Find the folloving:
x intercept(s)
y intercept
equation(s) of the vertical asymptote
Domain
Equation of the horizontal/oblique asymptote
location of hole(s) in the graph
end behavior

steve816 · Answer

I don't need you guys to find the answers I need you guys to refresh my memory and explain how to find each one! Help would be greatly appreciated.

campbell_st · Answer

so to find the x- intercepts solve $$x^2 + 12x + 12 = 0$$ but check its not an asymptote... to find the y-intercepts let x = 0 and solve for y vertical asymptotes are the place where the denominator is zero, so solve $$x^2 - 16 = 0$$ Domain, what values of x, can't you have in the denominator..? the curve has a horizontal asymptote since the degree of the numerator and denominator are both 2. so simplify $$\frac{x^2}{x^2} = ?$$ and if you get stuck just graph it using https://www.desmos.com/calculator

steve816 · Answer

Man thanks so much. You know everything xD