Question

Explain how to write a function rule from the table below. Then write a function rule.

X: 2, 4, 6
Y: 1, 0, -1

Answer 1

i would do newtons method; setup an equation has roots in X, to solve for Y

that way the X parts zero out the coefficients 1 by 1 and you end up with a solution

Answer 2

Can u help me, i dont know how to do that

Answer 3

I can try one sec

Answer 4

um well first of do u know the equation or tht wht ur trying to find?

Answer 5

yah, X: 2, 4, 6
Y: 1, 0, -1

Answer 6

One second, I think I know

Answer 7

newtons way:
x-2=0, when x=2
x-4 = 0 when x=4
x-6 = 0 when x=6, use these to zero out the terms

y = a + b(x-2) + c(x-2)(x-4) + ... well the rest are zeros regardless


now let y be what it is when x is a value and solve for the a b c parts

Answer 8

other than that, you can try to fit it to some quadratic with a system of 3 equations in 3 unknowns

Answer 9

So:
Y-1=0
Y-0=0
Y--1=0

Answer 10

x is the input and y is the Dependant variable

Answer 11

to write a function, you need to the gradient and the y intercept

Answer 12

you need the gradient** Gradient, m= rise/run= -1/4

Answer 13

y intercept 1= -(1/4)* 2 + c

Answer 14

y = a + b(x-2) + c(x-2)(x-4)

when x=2, y=-1

-1 = a + b(2-2) + c(2-2)(x-4)
0 0

-1 = a


therefore:

y = -1 + b(x-2) + c(x-2)(x-4) ; let x=4, y=0

0 = -1 + b(4-2) + c(x-2)(4-4)
0
0 = -1 +2b ; b = 1/2


etc

Answer 15

1= -(1/2) + c

Answer 16

c = 1 +1/2 = 3/2
Therefore y= -1(1/4)x + 3/2

Answer 17

I've made a mistake the gradient is -1/2 and thus the y-intercept is 2

Answer 18

lol, i got my -1 and 1 mixed around ... but Jess idea works out too

Answer 19

making our function y= -(1/2)x +2 Is that clear?

Answer 20

SO the function rule is 1= -(1/2) + c

Answer 21

The function would be y= -(1/2)x +2

Answer 22

y = 1 - (x-2)/2 + c(x-2)(x-4), let x=6 and y=-1, solve for c

-1 = 1 - (6-2)/2 + c(6-2)(6-4)

-2 = -2 + c(4)(2)

0 = 8c, c=0

therefore:

y = 1 - (x-2)/2
= 1 - x/2 +1
= -x/2 + 2

Answer 23

exactly

Answer 24

oh ok

Answer 25

and that ^ is how u right a function rule for the table?

Answer 26

We're done now, I hope I've helped :)

Answer 27

lol I sat back and watched them wrk it out and they got it right man/girl

Answer 28

which one is how to write a function rule?

Answer 29

@Jesstho.-.

Answer 30

Scroll up, I've explained everything :)

Answer 31

thanks :D

Answer 32

No problem :)