Question

Find the rule for the function
x, -1, 0, 1, 2
y, 3, 1, 1/3, 1/9

Answer 1

The function is y =
`(1)/(3)^(x)`

This can be found by using the base equation for exponential y =
`ab^(x)`. Now we can use the second ordered pair (0, 1) to find the value of a.

y =
`ab^(x)`

1 =
`ab^(0)`

1 = a(1)

1 = a

Now that we have a, we can solve for b using any other ordered pair.

y =
`ab^(x)`

`(1)/(3)` =
`(1)b^(1)`

`(1)/(3)` = (1)(b)

`(1)/(3)` = b

Now we can use these in the same equation.

y =
`(1)/(3)^(x)`