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 = $\frac{1}{3}^{x}$

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 = $ab^{x}$

$\frac{1}{3}$ = $(1)b^{1}$

$\frac{1}{3}$ = (1)(b)

$\frac{1}{3}$ = b

Now we can use these in the same equation.

y = $\frac{1}{3}^{x}$