A step by step tutorial on graphing and sketching arccos(x) functions and also the domain and range of these functions and other properties are discussed.
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Graph, Domain and Range of arccos(x)In what follows, arccos(x) is the inverse function of f(x) = cos(x) for 0 ? x ? ?.The domain of y = arccos(x) is the range of f(x) = cos(x) for 0 ? x ? ? and is given by the interval [-1 , 1]. The range of arccos(x) is the domain of f which is given by the interval [0 , ?]. The graph, domain and range of both f(x) = cos(x) for 0 ? x ? ? and arccos(x) are shown below. A table of values of arccos(x) can made as follows:
Example 1Find the domain and range of y = arccos(x - 1) and graph it.
Solution to Example 1
The value of x is calculated from the value of x - 1. For example when x - 1 = -1, solve for x to find x = 0 and so on. The domain is given by the interval [0,2] and the range is given by the interval [0,?] The three points will now be used to graph y = arccos(x - 1).
Example 2Find the domain and range of y = 2 arccos(x + 1) and graph it.
Solution to Example 2
We use the 3 key points in the table as follows, then find the value 2 arccos(x + 1) and x.
domain = [-2,0] , range = [0 , 2 ?]
Example 3Find the domain and range of y = - arccos(x - 1) and graph it.
Solution to Example 3
We use the 3 key points in the table as follows, then find the value - arccos(x - 1) and x.
domain = [0 , 2] , range = [- ? , 0] More References and Links to GraphingGraphing Functions
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