how to determine sign of a function

Answer 1

To determine the sign of a function, you need to examine the value of the function at different points on its domain. Here are the steps to follow:

1. Identify the function whose sign you want to determine. For example, suppose you have the function f(x).

2. Choose a point on the domain of the function. It can be any value within the domain. Let's say you choose x = a.

3. Substitute the chosen value (a) into the function and evaluate it. Find f(a).

4. Repeat steps 2 and 3 for other points on the domain if needed.

5. Analyze the evaluated values:

- If f(a) is positive (+), the function f(x) is positive (+) on the interval that includes the point a.
- If f(a) is negative (-), the function f(x) is negative (-) on the interval that includes the point a.
- If f(a) is zero (0), it means the function either changes sign at that point or has a stationary point (e.g., a local maximum or minimum).

6. Use the sign information obtained from step 5 to determine the sign of the function on different intervals of its domain.

Note: The intervals between the points you chose need to be analyzed individually to determine the function's sign over each interval.

Keep in mind that this method works for continuous functions, meaning no jumps or discontinuities within the domain. For functions with discontinuities, the sign determination may be more complex, requiring additional considerations.