The exploration is carried out by analyzing the effects of the parameters a, b, c and d included in the definition of arcsin as follows
f(x) = a arcsin(b x + c) + d
Interactive Tutorial
Change parameters a, b, c and d and click on the button 'draw' in the left panel below.
 Set the parameters to a = 1, b = 1, c = 0 and d = 0 to obtain
f(x) = arcsin(x)
Check that the domain of arcsin(x) is given by the interval [1 , 1] and the range is given by the interval [π/2 , +π/2](π/2 is approximately 1.57).
 Change parameter a and note how the graph of arcsin changes (vertical compression, stretching, reflection). How does it affect the range of the arcsin function?
Does a change in parameter a changes the domain of arcsin?
 Change parameter b and note how the graph of arcsin changes (horizontal compression, stretching). Does a change in b affect the domain of arcsin? range?
 Change parameter c and note how the graph of arcsin changes (horizontal shift). Does a change in c affect the domain of arcsin? range?
 Change parameter d and note how the graph of arcsin changes (vertical shift). Does a change in d affect the range of arcsin? domain?
 If the range of arcsin(x) is given by the interval [π/2 , π/2] what is the range of a*arcsin(x)? What is the range of a*arcsin(x)+ d?
 What is the domain and range of a*arcsin(bx + c)+ d?
Exercises
 Find the domain and range of f(x) = arcsin(x  1)  2 and graph f.
 Find the domain and range of g(x) = arcsin(x + 1) + 2 and graph g.
 Find the domain and range of h(x) = 2arcsin(x + 1) 1 and graph h.
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