Question

The function f(x) = 2x + 4 is restricted to a domain interval of -2 to 2. Is the domain over the interval continuous or discrete, and what is the range of the function?

A. Domain is discrete; Range: -3 to 3
B. Domain is continuous; Range: -3 to 3
C. Domain is discrete; Range: 0 < f(x) < 8
D. Domain is continuous; Range: 0 < f(x) < 8

Answer 1

The domain of the function is continuous in the given interval and the range is -3 to 8.

Step-by-step explanation:

The domain of the function f(x) = 2x + 4 in the given interval is continuous because all real numbers from -2 to 2 are included. This means that the function is defined for every value within the interval.

The range of the function can be determined by finding the minimum and maximum values it can take. Since the coefficient of x is positive (2 > 0), the function is increasing and the minimum value occurs at x = -2 and the maximum value occurs at x = 2. Plugging these values into the function, we find the range is -3 to 8.