Question

hi

Answer 1

find the rule for this function
(0,0) (1,0.5) (2,2) (3, 4.5) (4,8)

Answer 2

Okay, okay.... I am assuming that these are \(coordinates\) yes?

Answer 3

yes

Answer 4

Explain to me how this is a function?

Answer 5

That is just a jumbling of coordinates.......

Answer 6

there are no repeating values in x

Answer 7

each ordered pair represents a function. write a rule that represents the function.

Answer 8

how many values does y go up?

Answer 9

dosent say

Answer 10

no i asked you, calculate it..

Answer 11

oh

Answer 12

um i see all values somehow lead to 0.5 but i dont understand because 1 times 0.5 = 0.5 but 2 times 0.5 is 1

Answer 13

nooo like the difference between the y's
you have 0.5 then 2 so there's a difference of 1.5
then you have 2 and 4.5 there's a diff. of 2.5
then you have 4.5 and 8 there's a diff. of 3.5
so every next x it would go up by next number when it comes to y


does that make since?!?!?! >.<

Answer 14

oh a that makes sense

Answer 15

so try and figure out how to tye in what i explained into an equation for the y-intercept

Answer 16

i got y= x+1.5

Answer 17

Slope is defined as,

\(\displaystyle \frac{\Delta y}{\Delta x}~or~\frac{change~in~y}{change~in~x}\)

Answer 18

im not doing slope

Answer 19

I think that's right! not positive but yeaaaa

Answer 20

For every one that x changes, how much did the y change?

Answer 21

by 1.5

Answer 22

And the line started at (0,0) so there will be no y intercept. It will be in the form

y=mx

Now, what do you think?

Answer 23

ok thanks alot

Answer 24

(0,0) (1,0.5) (2,2) (3, 4.5) (4,8)

\[y=a+b(r_1-x)+c(r_1-x)(r_2-x)+d(r_1-x)(r_2-x)(r_3-x)+...\]

\[y=a+b(0-x)+c(0-x)(1-x)+d(0-x)(1-x)(2-x)+...\]
when x=0, y=x
\[0=a+b(0-0)+c(0-0)(1-0)+d(0-0)(1-0)(2-0)+...\]
\[0=a\]

when x=1, y=.5
\[.5=b(0-1)+c(0-1)(1-1)+d(0-1)(1-1)(2-1)+...\]
\[.5=-b+0~:~b=-.5\]

when x=2, y=.2
\[2=-.5(0-2)+c(0-2)(1-2)+d(0-2)(1-2)(2-2)+...\]
\[2=1-2c+0~:~c=-.5\]

etc ...

Answer 25

its only a line of the difference in the y parts is constant from one point to the next

Answer 26

one way to solve this is with a matrix of 5 equations in 5 unknowns

or 4 if you want to have a 0 y intercept

Answer 27

x^4a + x^3b + x^2c +xd + e = y

(0,0) (1,0.5) (2,2) (3, 4.5) (4,8)

0^4a + 0^3b + 0^2c +0d + 1 = 0
1^4a + 1^3b + 1^2c +1d + 1 = .5
2^4a + 2^3b + 2^2c +2d + 1 = 2
3^4a + 3^3b + 3^2c +3d + 1 = 4.5
4^4a + 4^3b + 4^2c +4d + 1 = 8

row reduce the coefficient matrix to define the abc parts

Answer 28

.5x^2 seems to suffice

Answer 29

if you had been given options, it would have been a simple mater of testing the points ...