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.

Graph, Domain and Range of arccos(x)In what follows, arccos(x) is the inverse function of f(x) = cos(x) for 0 ≤ x ≤ π.The domain of y = arccos(x) is the range of f(x) = cos(x) for 0 ≤ x ≤ π 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 , π]. The graph, domain and range of both f(x) = cos(x) for 0 ≤ x ≤ π 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,π] 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 π]
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 = [ π , 0] More References and Links to GraphingGraphing Functions
