Let y = f(x) be a function with domain d = [−6, 10] and range r = [−8, 12]. find the domain d and range r for each function. assume f(6) = 12 and f(10) = −8. (enter your answers using interval notation.)
a) y = −2f(x)
b) y = |f(x)|
c) y = f(x + 2) − 3

a.Domain ,D=[-6,10]

Range ,R=[-24,16]

b.Domain,D=[-6,10]

Range=[8,12]

c.Domain=[-4,12]

Range=[-11,9]

Step-by-step explanation:

We are given that  be  a function with domain D=[-6,10] and range R=[-8,12].

Assume f(-6)=12, f(10)=-8

a.

We have to find the domain D and range R of the function.

Substitute f(-6)=12 then we get

Substitute f(10)=-8[/tex]

Domain remain same like domain  of given function.

Domain ,D=[-6,10]

Range ,R=[-24,16]

b.

We have to find the value of domain and range.

Domain,D=[-6,10]

Range=[8,12]

c.

Substitute x=-6 then

Substitute x=10

Then, we get

Domain=[-4,12]

f(-6)=12 then , we get

Substitute x=10

then, we get

Range of f(x)=Range f(x+2)

Range=[-11,9]