Give the equations of any vertical asymptotes for the graphs of the rational functions.
f(x)=(x-4)/(x²+7)
there are none since
x^2 + 7 ≠ 0
To find the vertical asymptotes of a rational function, follow these steps:
1. Set the denominator of the function equal to zero and solve for x. The values of x that make the denominator zero will give you the potential vertical asymptotes.
In the case of the rational function f(x) = (x - 4)/(x^2 + 7), we need to find the values of x that make the denominator, x^2 + 7, equal to zero.
x^2 + 7 = 0
2. This equation, x^2 + 7 = 0, has no real solutions since there is no value for x that will make x^2 equal to -7. Therefore, there are no vertical asymptotes for the graph of f(x) = (x - 4)/(x^2 + 7).
In other words, the graph of this function will never approach any vertical lines as x approaches certain values.