Question

How do you graph `y=-2(3^x)+5`? What is the `y`-intercept and the domain and range?

Answer 1

See below.

Explanation:

The y axis intercept occurs where x = 0.

`- 2(3^0) + 5 => -2(1) + 5 = color(blue)(3)`

The domain is all `RR` since there is no restrictions on `x`

Domain`-> {x in RR }`

For positive `x`:

as `x -> oo` , `-2(3^x) + 5 -> -oo`

For negative `x`:

`-2(3^x) + 5` becomes `-2(1/3^x) + 5`

as `x ->- oo`

`-2(1/3^x) + 5-> color(blue)(5)`

So range is:

`{y in RR | -oo< y <= 5}`
graph{-2(3^x) + 5 [-12.66, 12.65, -6.33, 6.33]}