Question

How to determine the domain of a function?

A) Check for vertical asymptotes
B) Find the x-intercepts
C) Evaluate the limit
D) Identify excluded values

Answer 1

To determine the domain of a function, you need to check for restrictions, find x-intercepts, evaluate limits, and identify excluded values.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. To determine the domain of a function, you can follow these steps:

1. Check for any restrictions on the function, such as the presence of vertical asymptotes or excluded values. These can limit the domain.
2. Find the x-intercepts of the function. These are the points where the function crosses the x-axis, and they help identify the range of x-values that the function covers.
3. Evaluate the limit as x approaches certain values, such as infinity, to see if the function is defined for those values.
4. Identify any excluded values, such as the values that would result in division by zero or taking the square root of a negative number. These values are not part of the domain.

By using these steps, you can determine the domain of a function.