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The domain of the provide function where the function is defined is x less than the number three.
<h3>What is the domain of the function?</h3>Domain of a function is the set of all the possible input values which are valid for that function.
The function given in the problem is,
The above function is the function of logarithm. For the logarithmic function, it is defined for all the real numbers except 0.
Thus, the function should be greater than zero as,
Change the sign of both side, by changing the inequality,
Thus, the domain of the provide function where the function is defined is x less than the number three.
Learn more about the domain of the function here;
Answer:
- L(t) = 727.775 -51.875cos(2π(t +11)/365)
- 705.93 minutes
Step-by-step explanation:
a) The midline of the function is the average of the peak values:
(675.85 +779.60)/2 = 727.725 . . . minutes
The amplitude of the function is half the difference of the peak values:
(779.60 -675.85)/2 = 51.875 . . . minutes
Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.
Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.
Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.
Our formula is ...
L(t) = 727.775 -51.875cos(2π(t +11)/365)
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b) L(55) ≈ 705.93 minutes
The left side was cut out but x will be on top and 5 in the lower square. The last one is the answer.
