A constant function is a type of mathematical function where every output value is the same, regardless of the input value. This means that the graph of a constant function is a horizontal line.
To prove continuity for a constant function using ε-δ definition, we need to show that for any ε > 0, there exists a δ > 0 such that for all x within δ of the given input value, the output values do not deviate from the constant value by more than ε.
No, a constant function cannot be discontinuous as it always has the same output value for any given input value. Therefore, it satisfies the definition of continuity at every point.
A constant function has a constant output value regardless of the input value, while a linear function has a constant rate of change (slope) between the input and output values. In other words, a linear function is a straight line, while a constant function is a horizontal line.
The ε-δ definition allows us to mathematically prove the continuity of a function at a specific point. It provides a precise and rigorous way to show that a function is continuous at a given point, rather than relying on visual inspection or intuition.