Question

(x + n)If this is the graph of f(x) = a+k, then:

A. The domain is (h, c), and the range is (-...).
B. The domain is (-00,), and the range is (k,co).
C. The domain is (h,00), and the range is (k.).
D. The domain is (-0,), and the range is (h,0).

Answer 1

The graph of a constant function f(x) = a + k is a horizontal line, and since it is specified that 0 ≤ x ≤ 20, the function has a domain of [0, 20]. The range is the single value {k} as the function outputs this constant value across its entire domain.

Step-by-step explanation:

If the graph of f(x) = a + k is a horizontal line, this means that the function's output does not depend on the input x. Therefore, f(x) is a constant function and its graph is a horizontal line at the height k, where k is the constant value. Since the question specifies a domain of 0 ≤ x ≤ 20, the function is defined only for x values within this interval.

Accordingly, the domain of function f(x) is the set of all x values for which the function is defined, which in this case is the interval from 0 to 20 (inclusive). Hence, the correct domain is [0, 20]. The range of the function is the set of all possible output values, which is just k, the constant value of the function across its domain. Therefore, the range is the set containing only this single value {k}.