Question

The function modeled by the equation f(x) = 3x + 4 What is the range of function when domain is \ -2,3,5\ \ -6,19,29\ \ 20,19,29\ { 10,19,29\ \ 2,11,29\

Answer 1

`D=\{-2,3,5\}\\\\R=\{-2,13,19\}`

`D=\{-6,19,29\}\\\\R=\{-14,61,91\}`

`D=\{20,19,29\}\\\\R=\{64,61,91\}`

`D=\{10,19,29\}\\\\R=\{34,61,91\}`

`D=\{2,11,29\}\\\\R=\{10,37,91\}`

Explanation:

The range of a function is the set of all possible dependent values that the function can produce. In order to find the range for the given conditions, we need to evaluate every value of the domain.

When domain is:

`D=\{-2,3,5\}`

`f(-2)=3(-2)+4=-6+4=-2\\f(3)=3(3)+4=9+4=13\\f(5)=3(5)+4=15+4=19`

The range is:

`R=\{-2,13,19\}`

When domain is:

`R=\{-14,61,91\}`

`f(-6)=3(-6)+4=-18+4=-14\\f(19)=3(19)+4=57+4=61\\f(29)=3(29)+4=87+4=91`

The range is:

`R=\{-14,61,91\}`

When domain is:

`D=\{20,19,29\}`

`f(20)=3(20)+4=60+4=64\\f(19)=3(19)+4=57+4=61\\f(29)=3(29)+4=87+4=91`

The range is:

`R=\{64,61,91\}`

When domain is:

`D=\{10,19,29\}`

`f(10)=3(10)+4=30+4=34\\f(19)=3(19)+4=57+4=61\\f(29)=3(29)+4=87+4=91`

The range is:

`R=\{34,61,91\}`

When domain is:

`D=\{2,11,29\}`

`f(2)=3(2)+4=6+4=10\\f(11)=3(11)+4=33+4=37\\f(29)=3(29)+4=87+4=91`

The range is:

`R=\{10,37,91\}`

Answer 2

Answer: The range are

(-2, 13 , 19)

(-14, 61, 91)

(64, 61, 91)

(34, 61, 91)

(10, 34, 91)

Explanation:

f(x) = 3x + 4

Substitute the domain into the function above.

when domain are \ -2,3,5\

F(-2) = 3(-2) + 4 = -2

F(3) = 3(3) + 4 = 13

F(5) = 3(5) + 4 = 19

Range = -2, 13 , 19

When domain are \ -6,19,29\

f(x) = 3x + 4

F(-6) = 3(-6) + 4 = -14

F(19) = 3(19) + 4 = 61

F(29) = 3(29) + 4 = 91

Range = -14, 61, 91

When domain are \ 20,19,29\

f(x) = 3x + 4

F(20) = 3(20) + 4 = 64

F(19) = 3(19) + 4 = 61

F(29) = 3(29) + 4 = 91

Range = 64, 61, 91

When domain are 10,19,29\

f(x) = 3x + 4

F(10) = 3(10) + 4 = 34

F(19) = 3(19) + 4 = 61

F(29) = 3(29) + 4 = 91

Range = 34, 61, 91

When domain are \ 2,11,29

f(x) = 3x + 4

F(2) = 3(2) + 4 = 10

F(11) = 3(11) + 4 = 34

F(29) = 3(29) + 4 = 91

Range = (10, 34, 91)