How do you find the domain and range of #y=4-x^2#?

1 Answer
Joel Kindiak
Aug 29, 2015

Graph it

graph{4-x^2 [-10, 10, -5, 5]}

Explanation:

You'll notice that depending on your domains (denoted as #D_f#, you get different ranges (denoted as #R_f#):

#D_f = [–a, 0]# or #[0, a]# or #[–a, a]# where #a>0#, #R_f=[4-a^2,4]#
#D_f = [a, b]# where #a,b>0# and #b>a#, #R_f=[4-b^2,4-a^2]#
#D_f = [a, b]# where #a,b<0# and #b>a#, #R_f=[4-a^2,4-b^2]#
#D_f = [a, b]# where #a<0, b>0# and #abs(b)>abs(a)#, #R_f=[4-b^2,4]#
#D_f = [a, b]# where #a<0, b>0# and #abs(a)>abs(b)#, #R_f=[4-a^2,4]#

Ultimately however, since there is no restriction, the assumption is #D_f=RR#, thus #R_f=(–infty,4]#

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