How do you find the domain and range of y=4-x^2y=4x2?

1 Answer
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_fDf, you get different ranges (denoted as R_fRf):

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]