Question

whats the domain and range of y=x^2-9 in interval notation

Answer 1

@Hero if you could help it would be appreciated

Answer 2

Are there any restrictions for the domain? In other words, is there a value of x that we can put into the equation that will result in a false or undefined value for y?

Answer 3

yes it would be three and then would we put it in the round bracket system or is there another way for the domain

Answer 4

If we put 3 in place of x, what would be the false value of y?

Answer 5

0

Answer 6

So when x = 3, y = 0 which means y is false? So if y = 0, that means y is false?

Answer 7

yes

Answer 8

No, y can equal zero. Just because y = 0 does not mean the value is false. y can equal zero.

Answer 9

so would it be all real numbers (-infinity,infinity)

Answer 10

The domain is all real numbers, correct. What about the range? Are there any restrictions on the domain?

Answer 11

no

Answer 12

Are you sure about that? What happens when y = -1? Can we solve for x?

Answer 13

\(\bf y=x^2-9 \implies y=(x-{\color{brown}{ 0}})^2{\color{brown}{ -9}}\)

Answer 14

no

Answer 15

Actually, we are able to solve for x when y = -1.

Answer 16

if x is has a decimal value also i guess

Answer 17

If y = -1 then:

-1 = x^2 - 9
9 - 1 = x^2
8 = x^2
x = + or - sqrt(8)

Answer 18

But what about if y = -10?

Answer 19

x would be undefined

Answer 20

or would it be 1i

Answer 21

i mean i could we use imaginary numbers

Answer 22

When it comes to domain and range, by default, it is implied that we are speaking in the realm of real numbers unless otherwise specified.

Answer 23

What we know at this point is that y = -10 is undefined, but y = -9 is defined. Knowing this, what is the range of y?

Answer 24

(-10,infinity)

Answer 25

Range -> [-9, infinity)

Answer 26

ya i see what i did wrong thank you again for your help i appreciate the time you take to assist me and hope you have a good day @Hero