if the function h has a period of 3, which of the following could be a portion of the graph of h in the xy…
if the function h has a period of 3, which of the following could be a portion of the graph of h in the xy - plane? a b
Answer
Explanation:
Step1: Recall period - definition
A periodic function (h(x)) with period (T = 3) satisfies (h(x)=h(x + 3)) for all (x) in the domain of (h). This means the graph of the function repeats itself every 3 units along the (x) - axis.
Step2: Analyze option A
In option A, the distance between two consecutive peaks (or troughs) is 4 units. For example, the peak at (x=-4) and the peak at (x = 0) has a horizontal distance of 4 units. So, the period of the function in option A is 4, not 3.
Step3: Analyze option B
In option B, the distance between two consecutive peaks (or other corresponding points) is 3 units. For example, if we consider the peaks, the horizontal distance between two consecutive peaks is 3 units. So, the function in option B has a period of 3.
Answer:
B.