asymptotes, x and y intercepts, range and domain of
f(x)= $\frac{1}{x-4}$
You asked:
Find any horizontal, vertical, or oblique asymptotes, any x-intercepts, any y-intercepts, the range, and the domain of \(f\left( x \right) = \frac{1}{x - 4}\)
MathBot Answer:
\(f(x)=\frac{1}{x - 4}\) has a horizontal asymptote at \(y=0\).
\(f(x)=\frac{1}{x - 4}\) has a vertical asymptote at \(x=4\).
\(f(x)=\frac{1}{x - 4}\) does not have any oblique asymptotes.
\(f(x)=\frac{1}{x - 4}\) does not have an x-intercept.
The y-intercept of \(f(x)=\frac{1}{x - 4}\) is \(y = - \frac{1}{4}\)
The range of \(f(x)=\frac{1}{x - 4}\) is \(\left(-\infty, 0\right) \cup \left(0, \infty\right)\).
The domain of \(f(x)=\frac{1}{x - 4}\) is \(\left(-\infty, 4\right) \cup \left(4, \infty\right)\).