Find the domain and range of the functions?

1)

Domain. The two pieces are defined for all reals x, so

Domain=(-oo,+oo)

Range

1° piece

4x-10 assumes increasing values as x increases so:

• Maximum value is for x=2 that is f(2)=-2

• Inferior value is when x→-oo that is -oo

The range of the first piece is (-oo,-2)

2° piece

4-1/2x assumes deceasing values as x increases so:

• Superior value is for x=2 that is f(2)=3 but 2 is NOT reached so 3 is to be excluded

• Inferior value is when x→+oo that is -oo

The range of the second piece is (-oo,3)

The range of the interior function will be the Union of the two sets that is (-oo,-3)

Range=(-oo,-3)

2)

Domain=(-oo,2) U [4,7)

Range=[-2,+oo)

-2 belongs to range in fact f(-7) = -2

1) . domain is as given while the range is ( - ∞ , 3 ]

2) . using the graph ( only ) the domain is ( ≈ - 10.25 , 2) U [4 , 7)......and range is [ - 2 , 11 ]