Question

Which function has a range of y < 3?
y=3(2)x
y=2(3)x
y=-(2)x +3
y = (2)x - 3

Answer 1

Answer:

$\large\boxed{y=-(2)^x+3}$

Step-by-step explanation:

$\text{A function y = a(b)}^x\ \text{has a range:}\\\\y<0\ \text{for}\ a<0\\\\y>0\ \text{for}\ a>0\\\\f(x)+n-\text{shift a graph}\ n\ \text{units up}\\f(x)-n-\text{shift a graph}\ n\ \text{units down}\\f(x+n)-\text{shift a graph}\ n\ \text{units to the left}\\f(x-n)-\text{shift a graph}\ n\ \text{units to the right}\\\\\text{We have the range}\ y<3.\ \text{Therefore}\ a<0\ \text{and}\ n=3.$