Question

REWARDING MEDAL ! PLEASE HELP
The set of ordered pairs represents a function. write a rule that represents the function.
(-2,10/9), (-1,4/3), (0,2), (1,4), (2,10)
i think i have to use the y=g^x rule here but im not sure
please and thank you

Answer 1

@whpalmer4

Answer 2

http://www.slideshare.net/mrzeidan/chapter-5-identifying-linear-functions

Answer 3

here some sites thst could help

Answer 4

This isn't a linear function, so you need to guess the form. Unfortunately, I can't help you—I'm going to be out until sometime tomorrow. Perhaps @mathmale can help you out.

Answer 5

Points on the graph include: (-2,10/9), (-1,4/3), (0,2), (1,4), (2,10)

You said, "I think i have to use the y=g^x rule.)

Let's try a slightly more complicated model of this function (called an "exponential function:" y=a*b^(cx):\[y=a*b ^{cx}\]
Our job is to determine the values of a, b and c, so that all 5 given data points satisfy the equation involving a, b and c. In other words, we have three equations in three unknowns, which constitutes enough information to enable us to solve for a, b and c.

Point #1: (-2,10/9): x=-2, y=10/9; these values are to be substituted into the model \[y=a*b ^{cx}:\]
\[\frac{ 10 }{ 9 } =a*b ^{c(-2)}.\]

Point #2: (0,2): x=0, y=2:
\[2=a*b ^{0}\rightarrow a=2\]

Answer 6

Do the same thing for one more point (you choose which one).

You'll end up with three equations in the unknowns a, b and c. Since a=2, you can substitute a=2 into the other two equations, reducing the number of unknowns to 2.
Now solve that system of two exponential equations for b and c.

Take your valures for a, b and c and substitute them into our model, y=a*b^(cx).

Answer 7

On second thought, I'd suggest you use the model (involving base e instead of base b) that follows: