Domain and Range of Transformed Functions
Find the domain and range of each function. Use interval notation unless there’s a more efficient
way to state it. A sketch may help, but is not mandatory.
Range is only affected by vertical transformations. Domain is only affected by horizontal
transformations.
1) f (x) = x D: x≥0
R:y≥0
2) f (x) = 4 x − 3 + 1 D:x≥3
R:y≥1
3) f (x) = x 2 D: All reals
R: y≥0
4) f (x) = −x 2 + 3 D: All reals
R: y≤3
5) f (x) = x 3 D: All reals
R: All reals
6) f (x) = −9 ( 3x − 5 ) − 1 D: All reals
R: All reals
7) f (x) = 2 x D: All reals
R: y>0
8) f (x) = −2 x + 1 D:All reals
R: y<1
9) f (x) = x D: All reals
R: y≥0
10) f (x) = x − 7 + 11 D: All reals
R: y≥11
11) f (x) = − x − 4 D: All reals R: y≤–4
12) f (x) = − x + 5 D: x≥0
R: 0≤y
13) f (x) = 3 − −x − 1 D: x≤–1
R: y≤3
3
14) The inverse of f (x) = 3− x − 10 D: x>–10
R: All reals