Question

Let y = f(x) be a function with domain D = [−8, 12] and range R = [−10, 14]. Find the domain D and range R for each function. Assume f(8) = 14 and f(12) = −10. (Enter your answers using interval notation.)

Not even sure where to start. Any help is appreciated

(a)
y = −2f(x)

(b)
y = f (1/2x)

Etc.

Answer 1

I can' t make any sense of it... didn't the question just GIVE you the domain and range? :/

Answer 2

oh okay, never mind.

Answer 3

Perhaps it was f(-8) = 14 ?

Answer 4

No, it is positive. Haha

Answer 5

That's annoying.
And the domain involves a -8?

Answer 6

Yeah. I guess it's referring to the parent function but I'm honestly not sure. No idea where to start haha

Answer 7

Maybe this can help you figure it out...the homework is online and it gives me 50 "tries", but it immediately gives me the answer if I get it wrong. The answer for the first function (A.) is this

Domain: [-8, 12]
Range: [-28, 20]

Answer 8

I know.
Here's a hint....
If f(x) is left unaltered (IE, you still see f(x) and not f(1/2x) or something)
then the domain is left as is.

Answer 9

in this case, domain is STILL [-8, 12]

Answer 10

Whatever you multiply to the f(x) itself, you multiply the range by that number.

See, the original range was [-10 , 14]
but you multiply everything by -2, so you get
[-28 , 20]

Answer 11

a) D: [-8,12], R[-28,20]

b) D: [-16, 24], R: [-10,14]

Answer 12

Long story short, whatever you multiply to f, you multiply that to the range.
Whatever you multiply with the x (inside of the f) you DIVIDE the domain by that number.

Answer 13

Thank you so much!