Question

Help! I have looked at so many lessons on writing exponential functions from a graph and nothing has helped.

Answer 1

y =
`8(-(1)/(2))^x`

Explanation:

Let the equation of the exponential function is,

y = a(b)ˣ

Since the graph of this function passes through two points
`(4, (1)/(2))` and (3, -1)

For the point
`(4, (1)/(2))`,

`(1)/(2)=a(b)^4` ---------(1)

For second point (3, -1),

-1 = a(b)³ ---------(2)

Divide equation (2) by equation (1),

`((1)/(2))/(-1)` =
`(a(b)^4)/(a(b)^3)`

`-(1)/(2)=b^((4-3))`

`-(1)/(2)=b`

From equation (2)

-1 =
`a(-(1)/(2))^3`

-1 =
`-(1)/(8)a`

a = 8

Therefore, equation of the exponential function will be,

y =
`8(-(1)/(2))^x`