Question

Which function has a range of y < 3?

y - 3(2)
y = 2(3)
O y=-(2)x+ 3
Oy- (2) * - 3

Answer 1

Given:

The range of a function is
`y<3`.

To find:

The function for the given range from the given options.

Solution:

In option A, the given function is:

`y=3(2)^x`

Here,
`(2)^x` is always greater than 0. So,
`3(2)^x` is also greater than 0, i.e.,
`y>0`.

In option B, the given function is:

`y=2(3)^x`

Here,
`(3)^x` is always greater than 0. So,
`2(3)^x` is also greater than 0, i.e.,
`y>0`.

In option C, the given function is:

`y=-(2)^x+3`

Here,

`(2)^x>0`

`-(2)^x<0`

`-(2)^x+3<0+3`

`y<3`

The range of this function is
`y<3`. So, option C is correct.

In option D, the given function is:

`y=(2)^x-3`

Here,

`(2)^x>0`

`(2)^x-3<0-3`

`y<-3`

The range of this function is
`y<-3`

Therefore, the correct option is only C.