An increasing function is a mathematical function where the value of the function increases as the input variable increases. In other words, as the value of x increases, the value of f(x) also increases.
To prove that a function is increasing, you can use the definition of an increasing function which states that for any two inputs x1 and x2, if x1 < x2, then f(x1) < f(x2). This means that for any two points on the function, the y-value of the first point will be less than the y-value of the second point.
Proving that a function is increasing is important because it allows us to make accurate predictions about the behavior of the function. It also helps us to understand the relationship between the input and output variables and can be used to solve real-world problems.
When a function has a positive value at a specific point, it means that the output or y-value of the function at that point is greater than zero. This indicates that the function is increasing at that particular point.
No, if a function is increasing, it cannot have a negative value at a specific point. This is because an increasing function by definition means that the value of the function increases as the input variable increases. Therefore, it cannot have a negative value at any point along the function.