Question

Write a rule for a nonlinear function such that y is negative when x = 1, positive when x = 2, negative when x = 3, positive when x = 4, and so on.

The entire problem confuses me. I have no idea what its even asking besides it wants an equation.

Answer 1

Also, will fan anf medal

Answer 2

\[y=(-1)^x \]

Answer 3

We know that a negative value is positive of all even exponents and negative for all odd exponents

Answer 4

Okay

Answer 5

So for like x=1
y = -1^-1??

Answer 6

What is an Equation?
An equation says that two things are equal. It will have an equals sign "=" like this:
\[x + 2 = 6 \]

Answer 7

well i know what an equation is.

Answer 8

That equations says: what is on the left (x + 2) is equal to what is on the right (6)
So an equation is like a statement "this equals that"

Answer 9

yeah

Answer 10

when x = 1
would y= -1?

Answer 11

\[ y= -1^{-1} \]
That's what you said. I think it is correct.

Answer 12

okay and when x=2
y = -2?

Answer 13

or would it be positve 2?

Answer 14

\[-2=-1^{2} \]

Answer 15

so it would be y = 2?

Answer 16

Yes

Answer 17

then when x=3
y=-3?

Answer 18

\[3=1^{3} \]

Answer 19

so it would be y = -3

Answer 20

Even exponents make the number positive and odd exponents make the number negative.

Answer 21

how come? i dont understand that

Answer 22

It's just a rule lol Im just following it

Answer 23

oh ok

Answer 24

okay so even=positive and odd=negative

Answer 25

i think i got it then

Answer 26

what that is basically saying is that when you plug in x = 1 for x, you get a negative number, which is true.
-1 raised to the 1 is still just negative one.
but if you square it, -1 becomes positive. (-1)(-1) = 1.
Similarly, with x cubed.
(-1)(-1) = 1 (-1) = -1. So you get a negative number again.

Answer 27

ohhh okay

Answer 28

that makes sense

Answer 29

thank you so much

Answer 30

:) glad I was able to help.

Answer 31

Fanned and medalled :)

Answer 32

:D Thanks