Final answer:
The domain of the function f(x) = 1/(x + 5) is all real numbers except x = -5. The function exhibits a vertical asymptote at x = -5, with the value of the function approaching positive infinity from the right and negative infinity from the left as x approaches -5.
Step-by-step explanation:
The domain of the function f(x) = \frac{1}{x + 5} is all real numbers except for x = -5, because the denominator becomes zero at x = -5 which would make the function undefined. To describe the behavior of the function at the value 'x' not in its domain using limits, we examine the function as x approaches -5 from both sides.
As x approaches -5 from the right (x > -5), the function values increase towards positive infinity, indicative of a vertical asymptote. Conversely, as x approaches -5 from the left (x < -5), the function values decrease towards negative infinity. This behavior shows that the function has a vertical asymptote at x = -5, and the domain is all real numbers except x = -5.
To illustrate, the limit of f(x) as x approaches -5 from the right is: lim_{x \to -5^+} f(x) = \infty, and from the left is: lim_{x \to -5^-} f(x) = -\infty.
The complete question is: content loaded
Find the domain of the function f. Use limits to describe the behavior of 'f'at value(s) of 'x' not in its domain.
f(x) = 1/(X + 5) is: