Find the 66th term of the arithmetic sequence 25, 10, -5
1 answer:
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Answer:
The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is .
The domain of the function is all real numbers and its range is between -4 and 5.
The graph is enclosed below as attachment.
Step-by-step explanation:
Let be the base formula, where
is measured in sexagesimal degrees. This expression must be transformed by using the following data:
(Period)
(Minimum)
(Maximum)
The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of radians. In addition, the following considerations must be taken into account for transformations:
1) must be replaced by
. (Horizontal scaling)
2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:
3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)
The new function is:
Given that ,
and
, the outcome is:
The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.
