Give the equations of any vertical asymptotes for the graphs of the rational functions.
f(x)=(x-4)/(x²+7)
look at the condition I stated for V.A.' s in the other post I answered for you, and see if you can answer this one.
To determine the equations of any vertical asymptotes for the given rational function f(x) = (x-4)/(x^2+7), we need to examine the denominator of the function.
In this case, the denominator is x^2 + 7. To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
x^2 + 7 = 0
This is a quadratic equation, but upon solving it, we observe that it has no real solutions. The quadratic term (x^2) is always positive, and adding 7 to it will still result in a positive value. Therefore, x^2 + 7 = 0 has no real solutions, which means there are no vertical asymptotes for the graph of the function f(x) = (x-4)/(x^2+7).
In this case, the graph of the rational function f(x) will have no vertical asymptotes.