Question

Find the domain of the function and use limits to describe the behavior of f at value(s) of x not in the domain.

a) Domain: All real numbers; f approaches infinity as x approaches the boundary of the domain.
b) Domain: All real numbers; f approaches zero as x approaches the boundary of the domain.
c) Domain: Excludes certain values of x; f has a limit at the excluded values.
d) Domain: Excludes certain values of x; f approaches infinity at the excluded values.

Answer 1

The domain of the function excludes certain values of x and the function has a limit at the excluded values.

Step-by-step explanation:

The correct answer is c) Domain: Excludes certain values of x; f has a limit at the excluded values.

The domain of a function refers to all possible values of x for which the function is defined. In this case, the function has excluded certain values of x, meaning there are certain x-values that are not allowed. However, at these excluded values, the function still has a limit. A limit describes the behavior of a function as it approaches a particular value or approaches infinity.

For example, consider the function f(x) = 1/x. The domain of this function excludes x = 0 because the value of y approaches infinity as x approaches zero. However, even though x = 0 is not in the domain, the function still has a limit at x = 0, which is infinity.