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 $y$.

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,

$(2)^x>0$

$-(2)^x$

$-(2)^x+3$

$y$

The range of this function is $y$. So, option C is correct.

In option D, the given function is:

$y=(2)^x-3$

Here,

$(2)^x>0$

$(2)^x-3$

$y$

The range of this function is $y$

Therefore, the correct option is only C.