D. Properties of Continuous Functions

Properties of Continuous Functions

The previous concept identified the characteristics of a function that is continuous at a point, and over an interval. Let’s explore Given two functions f(x) and g(x) that are continuous over a closed interval [a,b], would you expect that arithmetic operations on these two functions would also yield functions continuous over [a,b]?

Given the functions f(x)=x+3 and g(x)=−x+0.5 in the closed interval [−1,1], determine if f(x) and g(x) are continuous in the interval.

The functions f(x) and g(x) are shown in the graph. Inspection of each function graph and its equation, shows that they are each defined over the closed interval and the function limit at each point in the interval equals the function value at the point. Both functions are continuous in the interval.